Question

solve for x. round to the nearest tenth, if necessary.
(image of a right triangle bcd with right angle at c, cd = 13, angle at d is 72 degrees, bc = x)
answer attempt 1 out of 2
x =

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 72^{\circ}\), the opposite side to \(\theta\) is \(x\) and the adjacent side is \(13\). So, \(\tan(72^{\circ})=\frac{x}{13}\).

Step2: Solve for \(x\)

We know that \(\tan(72^{\circ})\approx3.0777\). Then \(x = 13\times\tan(72^{\circ})\). Substitute the value of \(\tan(72^{\circ})\): \(x=13\times3.0777\).
\(x = 40.0101\approx40.0\)

Answer:

\(40.0\)