Question

find x in the following triangle:

Explanation:

Step1: Find the length of the base segment adjacent to \(63^{\circ}\)

In the left - hand right - triangle, \(\cos63^{\circ}=\frac{\text{adjacent}}{\text{hypotenuse}}\). Let the adjacent side be \(a\).
\(a = 82\times\cos63^{\circ}\)
\(a\approx82\times0.4540 = 37.228\)

Step2: Find the length of the base segment adjacent to \(39^{\circ}\)

In the right - hand right - triangle, \(\cos39^{\circ}=\frac{\text{adjacent}}{\text{hypotenuse}}\). Let the adjacent side be \(b\).
\(b = 82\times\cos39^{\circ}\)
\(b\approx82\times0.7771=63.7222\)

Step3: Calculate \(x\)

\(x=a + b\)
\(x\approx37.228+63.7222\)
\(x\approx100.95\)

Answer:

\(x\approx101\)