Question

solve for x. round to the nearest tenth, if necessary.
triangle with right angle at t, side tu = 75, angle at u = 39°, side st = x
answer
attempt 1 out of 2
x = blank

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( STU \) (right - angled at \( T \)), we know angle \( U = 39^{\circ} \), side \( TU = 75 \), and we need to find side \( ST=x \). The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. For angle \( U \), the opposite side to \( \angle U \) is \( ST = x \) and the adjacent side is \( TU=75 \). So, \( \tan(U)=\frac{\text{opposite}}{\text{adjacent}}=\frac{x}{75} \).

Step2: Solve for \( x \)

We know that \( \tan(39^{\circ})=\frac{x}{75} \). To find \( x \), we can multiply both sides of the equation by 75. So, \( x = 75\times\tan(39^{\circ}) \).
Using a calculator, \( \tan(39^{\circ})\approx0.8098 \). Then \( x = 75\times0.8098 = 60.735 \). Rounding to the nearest tenth, we get \( x\approx60.7 \).

Answer:

\( 60.7 \)