Question

The area of a triangle is 1848. Two of the side lengths are 53 and 88 and the included angle is acute. Find the measure of the included angle, to the nearest tenth of a degree.

Answer 1

Area of triangle = 1848

Given the sides of the triangle

a =88

b=53

Using the formula of the area of a triangle

Substitute the values of the sides and area, then simplify

`1848=(1)/(2)*88*53*\sin \theta`
`\begin{gathered} 3696=4664\sin \theta \\ \sin \theta=(3696)/(4664) \\ \sin \theta=0.7925 \\ \theta=\sin ^(-1)0.7925=52.42^0 \\ \theta\approx52.4^{0\text{ }}(nearest\text{ tenth)} \end{gathered}`

Hence,

The value of the included angle to the nearest tenth degree is 52.4