Question

Find cos B exactly if a = 15, b = 11, and angle Cis a right angle

Answer 1

Answer:

Final answer is $\cos\left(B\right)=\frac{15}{\sqrt{346}}$ which is the last choice.

Step-by-step explanation:

In triangle ABC, we have been given a = 15, b = 11, and angle C is a right angle.

Now using those values, we need to find the exact value of cos B.

Apply Pythagorean formula:

$AB^2=AC^2+BC^2$

$AB^2=11^2+15^2$

$AB^2=121+225$

$AB^2=346$

$AB=\sqrt{346}$

Now apply formula of cos

$\cos\left(B\right)=\frac{BC}{AB}$

$\cos\left(B\right)=\frac{15}{\sqrt{346}}$

Hence final answer is $\cos\left(B\right)=\frac{15}{\sqrt{346}}$