5

Pythagorean ProblemsIn a right-angled triangle, the hypotenuse and the opposite sides are respectively cm and Whars the length of the adjacent side to 2 decimal pla...

Question

Pythagorean ProblemsIn a right-angled triangle, the hypotenuse and the opposite sides are respectively cm and Whars the length of the adjacent side to 2 decimal places? cmin length:

Pythagorean Problems In a right-angled triangle, the hypotenuse and the opposite sides are respectively cm and Whars the length of the adjacent side to 2 decimal places? cm in length:



Answers

The length of one leg of a right triangle is $1 \mathrm{cm}$ more than twice the length of the other leg. The hypotenuse measures $6 \mathrm{cm}$. Find the lengths of the legs. Round to one decimal place.

So for this problem, we need to find C. So we're going to use the pathetic goring there just as a reminder. Our failure in the room is a squared plus B squared equals C squared where C is always are high pot news which is across from the right angle and our A and R B R legs. So we have leg like high pod news. So we see that see, is what we're missing so we can go ahead and plug 13 in for a and nine and for B or you can do it the other way. Since they're both legs, you could go 13 for B and nine for a So we will have 13 squared plus nine square equals C squared notice will keep it as a variable since its are unknown. So 13 squared we get 169 plus nine squared, which is 81 He will see squared. Now we simply add 1 69 plus 81 will get 250 equals C squared. Awesome. So we found C squared. But that's not what we're looking for. We're looking for seat, so to find. See, we need to take the square root of C squared. Well, if we take the square root of C squared, we have to take the square root of 250. But the square root of 250 can be simplified, so let's go ahead and simplify that. So two numbers that multiply to 250 I'm gonna use 25 10. You neither of these air prime. So let's break him down. We have five times five, both of those air prime. So let's move on to the 10. We'll have five and two on both of those air prime. Now we're gonna look for pairs, so we have a pair of fives here so that could be brought out front. The five in the two, however, don't have a pair, so they have to stay on the inside. Now, let's just simplify the five times two and we'll get five Route 10 and that's what C equals

We're going to use the Pythagorean theorem to solve for C here. Since we have a right triangle, we can go ahead and use the stagnant there. So just as a reminder, the Pythagorean there miss a squared plus B squared. People see square where a is a leg B is a leg and C is the high pot news which is across from love, right angle. So now we can go ahead and plug in our legs so we can use is 12 and be as 10. So we have 12 square plus 10 squared. You will see squared Simplify those squares we'll get 144 plus 100 equals C squared. Now we'll add and get 244 equals C squared But we want c not C square. So to get see if we need to take the square root of C squared And if we take the square root of C square we also have to take the square root of 244. So we're going to take the square root of 200 and 40 for and we're going to simplify that. So we're gonna find two numbers that multiply to 244 I'm going to use to in 1 22 and to his prime. So that was done. But on 1 22 I'm going to use to and 61 and both of those air prime. So we're all done. Now we're gonna look for pairs, so we have a pair of twos, so that, too, is gonna be brought out front. And 61 does not have a pair, so it has to stay on the inside. So two square root of 61 is what we get before.

All right, We're going to use the battalion theory, um, to solve for B, since we have a right triangle to Susan. Reminder of Pythagorean Theorem is a squared plus B squared equals C squib where a is a leg B is a leg and C is the high pot news which is across from the right angle. So we have our A and we have our C and they want us to find B. So let's plug in our A and R C. So are a is seven squared plus B squared equals R. C is 11. So now we're gonna simple 57 squared is 49 plus B squared equals 11 squared, which is 121 Now we're going to subtract 49 from both sides so that we can get b squared alone. So we'll have be square equals 72 here which gets us be square. But we don't not be squared. We want be so forgiven b squared and we won't be. That means we need to take the square root of beasts were well, if we take the square root of b squared, then we also have to take the square root of 72. So over here, let's take the square root of 72. Someone find two numbers that multiply to 72. I'm gonna use nine and eight neither of those air prime. So we can simplify, then more for nine. And I'm gonna use three and three both of those air crimes. So we're done there for eight I'm going to use for and to two is prime, but four is not. So we can keep going on that two and two now, both of those Air prime. So we're all done now we're gonna find pairs. We have a pair of threes and a pair of twos, so three will come out and a two will come out this to does not have a pair, so it has to stay on the inside. So let's simplify three times to we will get a six, and then we have that route to, and this is what our B equals

All right here we are trying to find a Since we have a right triangle, we're going to use the Pythagorean theorem. Just as a reminder are the degree in Durham is any squared plus B squared equals C squared where a is a leg. Bia's a leg and C is the high pot news across from the right angle. So we have one leg and we have our high pot nous. But we are trying to find a so it's plug reason so we don't have our A so that will stay as a. That means RB, which is our other leg, is seven, and our see our pot news across from the right angle is nine. We'll simplify this. We have a squared plus 49 equals 81. Now we'll subtract 49 so that we can get a squared by itself. So a squared equals 32. Awesome, but we're not looking for a square. We're looking for a So to get a, we need to take the square root of a squared. If we take the square root of a square, we have to take the square root of 32. So let's simplify the square root of 32. Two numbers that multiply to 32 are going to be a and for neither of those air prime. So we can keep going. Eight will break down to two and four to his prime. So we're done there. But for Incan, break down to two and two and both of those air prime. So we're done there going back to this four. We can break that down to two times two and both of those Air prima's. Well, so now we're gonna look for pairs. So here I have a pair of twos and I have another pair of twos, and each of those will come out one in front. This two, however, does not have a pair, so it has to stay inside. So simplifying that two times two, we will get four route to, and that is what are able equal


Similar Solved Questions

3 answers
Let p(z) , 9(z) be continuous functions_ Consider the ODEy + py + qyLet y1 and yz be linearly independent solutions_ Show that the set of all solutions to this ODE gives rise to vector space. V_ Show that V from part (a) is an inner product space with inner product (f.9) f(0)g(o) + f'(0)g' (0) .
Let p(z) , 9(z) be continuous functions_ Consider the ODE y + py + qy Let y1 and yz be linearly independent solutions_ Show that the set of all solutions to this ODE gives rise to vector space. V_ Show that V from part (a) is an inner product space with inner product (f.9) f(0)g(o) + f'(0)g...
5 answers
Itan(x + iy) + il1 + ezyezy
Itan(x + iy) + il 1 + ezy ezy...
5 answers
006.tr77 Ortjunial Dutn Lt Kecnhteam Ye c4 chlditnin celmeters| AN(00 mlnttCe] |durertnUi 4 U-L eluos unbab dtneraad(e > 09 2)HlmatnIlnT€AKmnAnenDe >MLlateeeucumul
006.tr77 Ortjunial Dutn Lt Kecnhteam Ye c4 chlditnin celmeters| AN(00 mlntt Ce] |d urertn Ui 4 U-L eluos unbab dtneraad (e > 09 2) Hlmatn IlnT€A Kmn AnenDe >M Llateee ucumul...
5 answers
If2^ 172*1 y then which of the following i$ true? (A) X is a positive value (B) x IS negative value (C) X can either be positive Or negative value (D none of these
If2^ 172*1 y then which of the following i$ true? (A) X is a positive value (B) x IS negative value (C) X can either be positive Or negative value (D none of these...
5 answers
(0) Construct & scatterplot of the right foot temperature (v) versus the left foot temperature (r)E 1 1Leit Foot Temperature {"F)
(0) Construct & scatterplot of the right foot temperature (v) versus the left foot temperature (r) E 1 1 Leit Foot Temperature {"F)...
5 answers
Let f(r) be the function 2 + 41. Find the following:f(2)
Let f(r) be the function 2 + 4 1. Find the following: f(2)...
3 answers
It is said that Mendel proposed that the factor controlling any character is discrete and independent. This proposition was based on the(a) Results of $mathrm{F}_{3}$ generation of a cross.(b) Observations that the offsprings of a cross made between the plants having two contrasting characters show only one character without any blending.(c) Self-pollination of $mathrm{F}_{1}$ offsprings.(d) Cross-pollination of parental generations.
It is said that Mendel proposed that the factor controlling any character is discrete and independent. This proposition was based on the (a) Results of $mathrm{F}_{3}$ generation of a cross. (b) Observations that the offsprings of a cross made between the plants having two contrasting characters sho...
5 answers
In the figure; a metal wire of mass m 27.4 mg can slide with negligible friction on two horizontal parallel rails separated by distance d =2.82 cm The track lies in a vertical uniform magnetic field of magnitude 66.0mT.At time t = 0 s,device G is connected to the rails; producing constant current i = 5.88 mA in the wire and rails (even as the wire moves) At t = 58.7 ms, what are the wire's (a) speed and (b) direction of motion?(a) NumberUnits(b) to the left
In the figure; a metal wire of mass m 27.4 mg can slide with negligible friction on two horizontal parallel rails separated by distance d =2.82 cm The track lies in a vertical uniform magnetic field of magnitude 66.0mT.At time t = 0 s,device G is connected to the rails; producing constant current i ...
5 answers
On sides $A B, B C, C A$ of a triangle $A B C$ we draw similar triangles $A D B, B E C, C F A$, having the same orientation. Prove that triangles $A B C$ and $D E F$ have the same centroid.
On sides $A B, B C, C A$ of a triangle $A B C$ we draw similar triangles $A D B, B E C, C F A$, having the same orientation. Prove that triangles $A B C$ and $D E F$ have the same centroid....
5 answers
9) 5.52 gal 7 mL10)45,000 pg ug11)9.55x107 Hz 7 MHz1210.221 mL fl. 0z13)6000 revolutionslmin + revolutions/hour
9) 5.52 gal 7 mL 10)45,000 pg ug 11)9.55x107 Hz 7 MHz 1210.221 mL fl. 0z 13)6000 revolutionslmin + revolutions/hour...
5 answers
Problem 2. (9 pts each) Determine whether each integral is convergent or divergent. +o +oo 22e-r? dx ii dx Vz (9 + x)
Problem 2. (9 pts each) Determine whether each integral is convergent or divergent. +o +oo 22e-r? dx ii dx Vz (9 + x)...
5 answers
Question 1Whi one of the below relations is not transitive?A bc a nonemptv sct and the relation is slbset ofl LetLet 1{0, {0}, {0. {0}}} and € the relation is elemehtioiInoncmpiv sct Mcd UL (ne Lct C RA be the scL ofall functions from relhtan "divides" defined in C as follows: f divides 9 if f(a)/g(a) isa positive integer FLe e A!Letbe 2 relation on R_ defined as: € ~ yiflr _ y <1
Question 1 Whi one of the below relations is not transitive? A bc a nonemptv sct and the relation is slbset ofl Let Let 1 {0, {0}, {0. {0}}} and € the relation is elemehtioi Inoncmpiv sct Mcd UL (ne Lct C RA be the scL ofall functions from relhtan "divides" defined in C as follows: f...
5 answers
Let G = ZzeU(5): The identity of G is28O 12
Let G = ZzeU(5): The identity of G is 28 O 12...
5 answers
Aad nder 30f Cl; Concecmamor1 concentamon 8 } remnerture Ikobetathis rate TH Sonficant Ece (0.00120 $ 2ca,0,6) i 1 1 Your Pno8
Aad nder 3 0f Cl; Concecmamor 1 concentamon 8 } remnerture Ikobetathis rate TH Sonficant Ece (0.00120 $ 2ca,0,6) i 1 1 Your Pno8...
5 answers
NaOH, when mixed with HCl, will produce NaCl and H2O. What mass of sodium hydroxide must be used to produce 225g ofNaCl?
NaOH, when mixed with HCl, will produce NaCl and H2O. What mass of sodium hydroxide must be used to produce 225g of NaCl?...
5 answers
Calculate the higher derivative.cos2(t)
Calculate the higher derivative. cos2(t)...

-- 0.020979--