Question

find the value of x. round your final answer to the nearest tenth.

Explanation:

Step1: Identify the trigonometric ratio

Since it is a right - triangle, and we know an angle (\(52^{\circ}\)) and the hypotenuse (\(15\)), and we want to find the adjacent side \(x\) to the \(52^{\circ}\) angle. We use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Substitute the values into the formula

Here, \(\theta = 52^{\circ}\), adjacent \(=x\), hypotenuse \( = 15\). So, \(\cos(52^{\circ})=\frac{x}{15}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(15\): \(x = 15\times\cos(52^{\circ})\).
Using a calculator, \(\cos(52^{\circ})\approx0.6157\). Then \(x=15\times0.6157 = 9.2355\).

Answer:

\(x\approx9.2\)