Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

The triangle is right - angled, and we know an angle (\(34^{\circ}\)) and the hypotenuse (length = 20). The side \(x\) is adjacent to the \(34^{\circ}\) angle. The cosine of an angle in a right - triangle is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(34^{\circ})=\frac{x}{20}\).

Step2: Solve for \(x\)

To solve for \(x\), we can multiply both sides of the equation \(\cos(34^{\circ})=\frac{x}{20}\) by 20. So, \(x = 20\times\cos(34^{\circ})\). We know that \(\cos(34^{\circ})\approx0.8290\) (using a calculator). Then \(x=20\times0.8290 = 16.58\approx16.6\) (rounded to the nearest tenth).

Answer:

\(16.6\)