Question
Use the Pythagorean Theorem to find the length of the missing side Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominatorFind tan 0_23
Use the Pythagorean Theorem to find the length of the missing side Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator Find tan 0_ 2 3
Answers
Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle $B$. Rationalize denominators when applicable. $$ a=3, b=4 $$
Given this right triangle. We're going to find the third side And the six trillion metric ratios. We know a. Six and C. Is seven. So to find that missing leg were news. The pythagorean theorem and we get C squared minus B squared equals c squared minus a squared equals b square C. Is seven. So we get seven squared minus six squared equals b squared 49 -36 equals b squared 49 minus 36. Is 13 equals b squared square root both sides. And we get the square to 13 equals B. I'm going to leave it like that. There is no perfect square root for the square to 13. So we're going to leave it as a radical. Now we can find our trigger metric ratios. Let's label R. H. O. A. We're going from angle be my oh is the opposite side, farthest away from that angle. So there's my oh my A. Is the one right next to it. It's my adjacent side. And my age is the hypotenuse which is the longest side, straight across from the right angle. So here's my age now that we have Rh away. Let's figure out our trig And metric ratios sign of B. Sign is opposite over high partners. So we get the square root of 13/7. Co sign is adjacent over high partners. So we get 6/7, Tangent is opposite over adjacent. We get the square root of 13/7 over six. So sign B is square to 13/7. Co sign B is 6/7 And Tangent B is the square to 13/6. Cosi cannot be is the inverse of sign. So instead of opposite over high partners, we're gonna cake. Hi pot knows over opposite. We don't leave it radicals in the denominator. So I'm going to multiply the top and the bottom by the square to 13 And we get seven square roots of 13/13 C. Can't is the inverse of co sign. So instead of adjacent over hypotenuse, We're going to take high partners over adjacent and we get to see Canada B is 76. Co tangent is the inverse of tangent. So instead of opposite over adjacent, we're going to say adjacent over opposite. We're going to multiply the top and the bottom by the score to 13 to get rid of that radical. In the denominator We get six square it's a 13/13. Cosi cannot be a seven square, it's a 13/13 C. can be a 76 and cold call Tanja B is six squares of 13/13
In this question. We have to find the value off later on. We're going that panty die going through three. Now we know that can be found by taking. I'm in worse off Three therefore t die record 60 dignities. This is a very common value from the David. Off commented Momenta, please. Years please try to the foot on device through the people again. Then again.
Given this diagram, we're going to figure out the length of the third side and then the trig. And metric value is going from angle be were given C. And A. So we need to figure out the length of leg B. We're going to use the pythagorean theorem. And we get C squared minus a squared equals b squared. We get 10 squared minus three squared equals B squared. This gives us 100 -9 equals b squared. Would then get 91 equals B squared. Take the square root of both sides. And we get the square to 91 equals B. The square to 91 does not have a perfect square. So we're just gonna leave it as a square to 91. Going from angle B. We're not going to label R. H. 08. Hey, my age, my hypothesis is the longest side straight across from my right angle. So here's my age. My oh is the opposite side. All the way across, furthest away from my angle. So there's my oh leaving my A right here, it's the adjacent side, right next to the ankle. We're talking about sign is opposite over high partners. So we get the square root of 91/10. Co side is adjacent over high partners. So we get 3/10, Tangent is opposite over adjacent. So we get the square to 91/3. Co C. Can't is the inverse of sign. So instead of opposite over high partners, we get high partners over opposite. We do not leave radicals in the denominator. So we're going to multiply the top and the bottom by the squirt. In 91 We get 10 square with some 91/91. C can't is the inverse of coal sign. So instead of adjacent over high partners, we get high partners over adjacent 13th. Co tangent is the inverse of tangent. So instead of opposite over adjacent, we're gonna get adjacent over opposite. Again. We don't leave radicals in the denominator. So I'm going to multiply the top and the bottom by the square to 91, giving us three square to 91/91.
We're being asked to find the sign or were being asked to find fatal. Where the sign of faith A is equal to the square, the three over too well, the sign of 60 degrees is equal to root three or to their fourth. Eva is equal to 60 degrees.