Question

solve for x in the triangle. round your answer to the nearest tenth. triangle image: right triangle with one angle 64°, hypotenuse 17, leg x

Explanation:

Step1: Identify trigonometric ratio

The triangle is right - angled, with hypotenuse = 17 and angle = \(64^{\circ}\). We need to find the opposite side to the \(64^{\circ}\) angle (which is \(x\)). The sine function is defined as \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(64^{\circ})=\frac{x}{17}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(64^{\circ})=\frac{x}{17}\) by 17: \(x = 17\times\sin(64^{\circ})\). Calculate \(\sin(64^{\circ})\approx0.8988\). Then \(x=17\times0.8988 = 15.2796\).

Step3: Round to nearest tenth

Rounding \(15.2796\) to the nearest tenth gives \(15.3\).

Answer:

\(15.3\)