Given a right triangle where one of the acute angles is $52°$ and the hypotenuse has a length of $208$, what is the length of the side adjacent to the $52°$ angle (to the nearest whole number)?

• A. $156$
• B. $104$
• C. $128$
• D. $116$

Answer: (C)

Verified step by step guidance

1. Identify the given information: the triangle is right-angled, one acute angle is 52\degree, and the hypotenuse length is 208.
2. Recall that the side adjacent to the 52\degree angle can be found using the cosine function, since cosine relates the adjacent side and the hypotenuse in a right triangle.
3. Write the trigonometric equation: \(\cos(52\degree) = \frac{\text{adjacent side}}{208}\).
4. Rearrange the equation to solve for the adjacent side: \(\text{adjacent side} = 208 \times \cos(52\degree)\).
5. Calculate the value of \(\cos(52\degree)\) using a calculator, multiply by 208, and then round the result to the nearest whole number to find the length of the adjacent side.