Find the exact value of the given trigonometric function of the angle $\theta$ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
Find: $\cos \theta$

A) $\frac { 8 } { 17 }$
B) $\frac { 15 } { 17 }$
C) $\frac { 8 } { 15 }$
D) $\frac { 15 } { 8 }$
E) $\frac { 17 } { 15 }$

Question

Find the exact value of the given trigonometric function of the angle $\theta$ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
Find: $\cos \theta$

A) $\frac { 8 } { 17 }$ 
B) $\frac { 15 } { 17 }$ 
C) $\frac { 8 } { 15 }$ 
D) $\frac { 15 } { 8 }$ 
E) $\frac { 17 } { 15 }$

Quizplus · Accepted Answer

We can use the Pythagorean Theorem to find the length of the missing side of the triangle, which is $\sqrt{17^2-8^2}=15$. Then, $\cos	heta=\frac{	ext{adjacent}}{	ext{hypotenuse}}=\frac{8}{17}$. Therefore, the answer is choice B, $\frac{15}{17}$.

Find the Exact Value of the Given Trigonometric Function of the Angle