Question

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

Explanation:

Step1: Identify trigonometric ratio

The triangle is right - angled. We know the hypotenuse (\(c = 9\)) and we want to find the adjacent side (\(x\)) to the angle of \(63^{\circ}\). The cosine function is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(63^{\circ})=\frac{x}{9}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(63^{\circ})=\frac{x}{9}\) by \(9\) to get \(x = 9\times\cos(63^{\circ})\). Calculate \(\cos(63^{\circ})\approx0.4540\). Then \(x=9\times0.4540 = 4.086\). Rounding to the nearest tenth, we get \(x\approx4.1\).

Answer:

\(4.1\)