Answer:
1) no, it is not a right triangle. 3² + 4² ≠ 25²
2) no, it is not a right triangle. 38² + 77² ≠ 86²
3) no, it is not a right triangle. 10² + 36² ≠ 37²
4) yes, it is a right triangle. 30² + 40² = 50²
5) yes, it is a right triangle. 8² + 15² = 17²
6) yes, it is a right triangle. 18² + 24² = 30²
7) no, it is not a right triangle. 5.3² + 7.9² ≠ 8.1²
8) yes, it is a right triangle. 10² + 24² = 26²
Im guessing it would be about 50 degrees
QUESTION 1
The tangent ratio is the ratio of the length of the opposite side of the length of the adjacent side.
From ΔVWX,
![\tan(X)=\frac{VW}{WX}](https://tex.z-dn.net/?f=%5Ctan%28X%29%3D%5Cfrac%7BVW%7D%7BWX%7D)
From ΔYZX,
![\tan(X)=\frac{YZ}{XZ}](https://tex.z-dn.net/?f=%5Ctan%28X%29%3D%5Cfrac%7BYZ%7D%7BXZ%7D)
![\therefore \tan(X)=\frac{VW}{WX}=\frac{YZ}{XZ}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Ctan%28X%29%3D%5Cfrac%7BVW%7D%7BWX%7D%3D%5Cfrac%7BYZ%7D%7BXZ%7D)
QUESTION 2
We use the tangent ratio to obtain;
![\tan(V)=\frac{Opposite}{Adacent}](https://tex.z-dn.net/?f=%5Ctan%28V%29%3D%5Cfrac%7BOpposite%7D%7BAdacent%7D)
![\tan(V)=\frac{WX}{VW}](https://tex.z-dn.net/?f=%5Ctan%28V%29%3D%5Cfrac%7BWX%7D%7BVW%7D)
QUESTION 3
From ΔVWX,
![\tan(X)=\frac{VW}{WX}](https://tex.z-dn.net/?f=%5Ctan%28X%29%3D%5Cfrac%7BVW%7D%7BWX%7D)
We take the inverse tangent of both sides to obtain;
![X=\tan^{-1}(\frac{VW}{WX})](https://tex.z-dn.net/?f=X%3D%5Ctan%5E%7B-1%7D%28%5Cfrac%7BVW%7D%7BWX%7D%29)
![\therefore \tan^{-1}(\frac{VW}{WX})=X](https://tex.z-dn.net/?f=%5Ctherefore%20%5Ctan%5E%7B-1%7D%28%5Cfrac%7BVW%7D%7BWX%7D%29%3DX)
QUESTION 4
From ΔVWX,
![\tan(V)=\frac{WX}{VW}](https://tex.z-dn.net/?f=%5Ctan%28V%29%3D%5Cfrac%7BWX%7D%7BVW%7D)
Taking the inverse tangent of both sides, we obtain;
![V=\tan^{-1}(\frac{WX}{VW})](https://tex.z-dn.net/?f=V%3D%5Ctan%5E%7B-1%7D%28%5Cfrac%7BWX%7D%7BVW%7D%29)
![\therefore \tan^{-1}(\frac{WX}{VW})=V](https://tex.z-dn.net/?f=%5Ctherefore%20%5Ctan%5E%7B-1%7D%28%5Cfrac%7BWX%7D%7BVW%7D%29%3DV)
QUESTION 5.
We know that
![\tan(V)=\frac{WX}{VW}](https://tex.z-dn.net/?f=%5Ctan%28V%29%3D%5Cfrac%7BWX%7D%7BVW%7D)
and
![\tan(X)=\frac{VW}{WX}](https://tex.z-dn.net/?f=%5Ctan%28X%29%3D%5Cfrac%7BVW%7D%7BWX%7D)
![(\tan X)(\tan V)=(\frac{VW}{WX})(\frac{WX}{VW}=1](https://tex.z-dn.net/?f=%28%5Ctan%20X%29%28%5Ctan%20V%29%3D%28%5Cfrac%7BVW%7D%7BWX%7D%29%28%5Cfrac%7BWX%7D%7BVW%7D%3D1)
QUESTION 6.
![\tan^{-1}(\frac{VW}{WX})=X](https://tex.z-dn.net/?f=%5Ctan%5E%7B-1%7D%28%5Cfrac%7BVW%7D%7BWX%7D%29%3DX)
![\tan^{-1}(\frac{WX}{VW})=V](https://tex.z-dn.net/?f=%5Ctan%5E%7B-1%7D%28%5Cfrac%7BWX%7D%7BVW%7D%29%3DV)
This implies that;
![\tan^{-1}(\frac{VW}{WX})+\tan^{-1}(\frac{WX}{VW})=X+V](https://tex.z-dn.net/?f=%5Ctan%5E%7B-1%7D%28%5Cfrac%7BVW%7D%7BWX%7D%29%2B%5Ctan%5E%7B-1%7D%28%5Cfrac%7BWX%7D%7BVW%7D%29%3DX%2BV)
QUESTION 7
![\tan 23\degree =0.4244](https://tex.z-dn.net/?f=%5Ctan%2023%5Cdegree%20%3D0.4244)
We round to the nearest 0.01 to obtain;
![\tan 23\degree =0.42](https://tex.z-dn.net/?f=%5Ctan%2023%5Cdegree%20%3D0.42)
QUESTION 8
![\tan 43\degree =0.9325](https://tex.z-dn.net/?f=%5Ctan%2043%5Cdegree%20%3D0.9325)
We round to the nearest 0.01 to obtain;
![\tan 43\degree =0.92](https://tex.z-dn.net/?f=%5Ctan%2043%5Cdegree%20%3D0.92)
QUESTION 9
![\tan ^{-1} 0.14=7.9696\degree](https://tex.z-dn.net/?f=%5Ctan%20%5E%7B-1%7D%200.14%3D7.9696%5Cdegree)
We round to the nearest 0.01 to obtain.
![\tan ^{-1} 0.14=7.97\degree](https://tex.z-dn.net/?f=%5Ctan%20%5E%7B-1%7D%200.14%3D7.97%5Cdegree)
QUESTION 10
![\tan ^{-1} 1=45.00\degree](https://tex.z-dn.net/?f=%5Ctan%20%5E%7B-1%7D%201%3D45.00%5Cdegree)
QUESTION 11
![\tan ^{-1} 0.14=7.97\degree](https://tex.z-dn.net/?f=%5Ctan%20%5E%7B-1%7D%200.14%3D7.97%5Cdegree)
This implies that;
![\tan 7.97\degree=0.14](https://tex.z-dn.net/?f=%5Ctan%207.97%5Cdegree%3D0.14)
QUESTION 12
![\tan ^{-1} 1=45.00\degree](https://tex.z-dn.net/?f=%5Ctan%20%5E%7B-1%7D%201%3D45.00%5Cdegree)
This implies that;
![\tan 45.00\degree=1](https://tex.z-dn.net/?f=%5Ctan%2045.00%5Cdegree%3D1)
Your answer is A. 7.2x10^-5
you can put both sides of the equation to the 4th power
![( \sqrt[4]{d - 15}) ^{4} = (2)^{4}](https://tex.z-dn.net/?f=%28%20%5Csqrt%5B4%5D%7Bd%20-%2015%7D%29%20%5E%7B4%7D%20%20%20%3D%20%282%29%5E%7B4%7D%20)
![d - 15 = 16](https://tex.z-dn.net/?f=d%20-%2015%20%3D%2016)
![d = 31](https://tex.z-dn.net/?f=d%20%3D%2031)