Question

question
solve for ( x ). round to the nearest tenth, if necessary.
triangle with right angle at u, angle at t is 40°, side tu is 64, side tv is x
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Use the cosine function

In a right - triangle \(TUV\) with \(\angle T = 40^{\circ}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 40^{\circ}\), adjacent side \(TU = 64\), and hypotenuse \(TV=x\). So, \(\cos40^{\circ}=\frac{64}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{64}{\cos40^{\circ}}\). Since \(\cos40^{\circ}\approx0.7660\), then \(x=\frac{64}{0.7660}\approx83.6\).

Answer:

\(83.6\)