Question

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

Explanation:

Step1: Find the base of the left triangle

Let the base of the left right - triangle be \(a\). We know that \(\tan(51^{\circ})=\frac{104}{a}\), so \(a = \frac{104}{\tan(51^{\circ})}\).
\(\tan(51^{\circ})\approx1.2349\), then \(a=\frac{104}{1.2349}\approx84.22\)

Step2: Find the base of the right triangle

Let the base of the right right - triangle be \(b\). We know that \(\tan(36^{\circ})=\frac{104}{b}\), so \(b=\frac{104}{\tan(36^{\circ})}\).
\(\tan(36^{\circ})\approx0.7265\), then \(b = \frac{104}{0.7265}\approx143.15\)

Step3: Find the value of \(x\)

Since \(x=a + b\), then \(x=84.22+143.15 = 227.37\)

Answer:

\(227.37\)