Question

find x correct to 2 decimal places. note: the triangle is not drawn to scale.

Explanation:

Step1: Find the adjacent side of \(58^{\circ}\)

Use the tangent function \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For the angle \(58^{\circ}\), \(\tan58^{\circ}=\frac{94}{a_1}\), so \(a_1 = \frac{94}{\tan58^{\circ}}\).

Step2: Find the adjacent side of \(40^{\circ}\)

For the angle \(40^{\circ}\), \(\tan40^{\circ}=\frac{94}{a_2}\), so \(a_2=\frac{94}{\tan40^{\circ}}\).

Step3: Calculate \(x\)

Since \(x=a_1 + a_2\), substitute the values of \(a_1\) and \(a_2\):
\(x=\frac{94}{\tan58^{\circ}}+\frac{94}{\tan40^{\circ}}\)
We know that \(\tan58^{\circ}\approx1.6003\), \(\tan40^{\circ}\approx0.8391\)
\(x=\frac{94}{1.6003}+\frac{94}{0.8391}\)
\(x\approx58.74 + 112.02\)

Answer:

\(x\approx170.76\)