Question

find the sine, cosine, and tangent of ∠x. simplify your answers and write them as proper fractions, improper fractions. sin(x) = cos(x) = tan(x) =

Explanation:

Step1: Find the length of side $WY$ using Pythagorean theorem

Let the length of $WY$ be $a$. By the Pythagorean theorem $a=\sqrt{85^{2}-36^{2}}=\sqrt{(85 + 36)(85 - 36)}=\sqrt{121\times49}=\sqrt{11^{2}\times7^{2}} = 77$.

Step2: Calculate $\sin(X)$

The sine of an angle in a right - triangle is the ratio of the opposite side to the hypotenuse. So $\sin(X)=\frac{WY}{XY}=\frac{77}{85}$.

Step3: Calculate $\cos(X)$

The cosine of an angle in a right - triangle is the ratio of the adjacent side to the hypotenuse. So $\cos(X)=\frac{WX}{XY}=\frac{36}{85}$.

Step4: Calculate $\tan(X)$

The tangent of an angle in a right - triangle is the ratio of the opposite side to the adjacent side. So $\tan(X)=\frac{WY}{WX}=\frac{77}{36}$.

Answer:

$\sin(X)=\frac{77}{85}$, $\cos(X)=\frac{36}{85}$, $\tan(X)=\frac{77}{36}$