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21. Find, t0 the nearest unit the length of te longer leg of a right triangle if the length of the hypotenuse is 8, and the measure of an acute angle is 22_...

Question

21. Find, t0 the nearest unit the length of te longer leg of a right triangle if the length of the hypotenuse is 8, and the measure of an acute angle is 22_

21. Find, t0 the nearest unit the length of te longer leg of a right triangle if the length of the hypotenuse is 8, and the measure of an acute angle is 22_



Answers

In $11-22,$ solve each triangle, that is, find the measures of the remaining three parts of the triangle to the nearest integer or the nearest degree.
In $\triangle A B C, a=8, \mathrm{m} \angle B=35,$ and $\mathrm{m} \angle C=55$

So here the high part news is given that is C. Is equal to 964 and one angle is given. So let's consider it us angle. Therefore year is equal to 17.6 degrees. So we need to find the longer legs. So we need to find both a. And b. And check whether which is which is the longer one. So here sign A. Is equal to. Yeah I see. That is yeah he is equal to 964 in do that is seeing do 7 17.6. That is the leg is, the length of the leg is To 91.5 approx. So now you have. Yeah. And see therefore according to buy the horse serum, B is equal to square root of C. Square minus a square. That is Cairo it off 964 sq to 91 point twice crap. That is B. Is equal to B. Is equal to 918 point 87 Therefore here B is still long at like

Hello, everyone. My name is Smith. Find them work to sort of a problem from chapter 14 Section seven on problem number 18. We have to find the measures of the remaining three parts of the triangle to the nearest India or to the nearest agrees. So let's draw other given dangle ABC, which looks like this. You get it taken. The Magnum is not drawn to the scale, but it is for our understanding. So they confined the animal A by using law, of course, I'd switches equals to be confined the sea within the laugh Courtside scores off. See physicals to a square plus B square mile s C square by two times a Toby I'm plugging in those will you is governess 20 Do square bless 18 square minus C square. There were about two times story, too. And don't worry, Dean cross multiplying So good eyes ready to pinto. 18. Hey, do cool cause I know see easy calls to 20 Do square place it is going Mina Cisco hiding C square on both sides. We'll get C Square less good times. 22. Cosette of sea is giving them cause a 1 30 It's when you do a square less hated square. We're losing. The calculator course of 1 30 is given by minus by antics 0.642 So C Square minus 0.642 into two times 22 in tow. 18. He's given by 7 92 22 square Let's 80 square Can we do to nurse Ay Tito? Eight. So C Square is equal to a general. Eight. Bless by 642 in tow. 7 92 So C Square can mitt it. Jonas 1316.5 1316.5 So sees equals to root of 1316.5 so she's approximately equals. Two. 36 point three. No confined co sign off a is equals two. The square plus C square My less a square by two times B c. The values. 18 square plus 36.3 square minus. Ready to square your eBay two times. 18 into 36.3. Yeah, for calculating me at this point, it did 58 courtside off a. So is better Dennis goes and in worse off by it. It five. It so equals 27 points for eight degrees So it is approximately. Go through cleanly seven Find five degrees bigger A will be And we know that some off all the gear and still a triangle is 1 80 Suddenly you're off End of a place is there a friend will be blessed 1,000,000 off embassy is when Edie Pretty 7.5 Bless, Major, if I will be you don't know less major off angle sees when Turkey so mission off and will be committed has won 80 minus 1 30 minus pretty soon 1.5 it is equal to Benito Burn five Similarly we can find So we have fallen. All the three paramour does we have will be major off and l A s 27.5 degrees Reynolds He's already given 1 30 degrees and no, he is ready to the 80 and see via phone. Nerd identities equals two 36.3

All right. So they've given us the triangles. The first thing I'm gonna do is I'm gonna draw that triangle. What? And we're told that we have, um, aside, A is 15 and we're told that B is 18 and that sees 60. But this is groups. Yeah, this is a This is B sissy. And so we were gonna call this little C. So the first thing I want to do is find this, see the side. So this is gonna be c squared equals, And we're going to use the lockup sons. So we're gonna do 15. Squared was eight. Things were minus two times 15 terms. 18 down the coast of the angle between them, which is 60. And so this is good. I'm gonna equal the square root of 549 minus 540. Closer, 60 When I do all that multiplication and so the sea is gonna equal about 17. Now that I have side sea I confined and was a and B. So I'm gonna use the lost son. So the son, uh, sorry. Over 15 equals the son of 60 over 17. If you cross, multiply and then do the inverse son. You know that A is gonna equal the inverse son of 15 son of 60 over 17 which is approximately 50 degrees. Then I can use the some there which says that the angles add up to 1 80 So 1 80 minus 60 minus 50 equals 110. Our angle. See? So what do I know? I know that a angle a is 50. I know that angle, See is 110 I guarantee. And that's what safety and succeed Chemical 70 and little C is gonna evil 17. And so the more than three missing parts to my journey.

All right. So they give us a triangle, ABC with some pieces and they tell us that be call this triangle ABC And they tell us be is 45 and C is 60 and that the side across from B is 25. So we need to find C and A along with angle. A first of all, no two angles. So Hughes angle some. We know that angle a is 75. Then we can use the law of sons so we can do this Son of 75 over a equals the sun Ah, 45/25. And if we cross, multiply and divide, we know that a is equal to 25 times the sign of 75 divided by the sine of 45. And so that's going to give us then about 34 for that side. We can repeat that with another Slav signs, and we can do. The son of 45/25 equals the son of 60 oversea and so C is equal to 25 son of 60 over the son of 40. And so C is equal to 31. So we know that angle a angle. A is 75. We know that Saad A is 34 and that side see is 31.


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