Question

calculator what is the value of x? enter your answer as a decimal to the nearest tenth in the box. ft

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 36^{\circ}\), the opposite side to the \(36^{\circ}\) angle is \(x\), and the adjacent side is \(15\) ft. So, \(\tan(36^{\circ})=\frac{x}{15}\).

Step2: Solve for \(x\)

We know that \(\tan(36^{\circ})\approx0.7265\). Then \(x = 15\times\tan(36^{\circ})\). Substitute \(\tan(36^{\circ})\approx0.7265\) into the equation: \(x=15\times0.7265 = 10.8975\).

Step3: Round to the nearest tenth

Rounding \(10.8975\) to the nearest tenth. The digit in the hundredth place is \(9\), so we round up the digit in the tenth place. \(10.8975\approx10.9\).

Answer:

\(10.9\)