Question

The area of a triangle is 5. two of the sides lengths are 4.1 and 2.5 and the included angle is obtuse. find the measure of the included angle, to the nearest tenth of a degree.

Answer 1

Given data:

The given area of the triangle is A=5.

The first side given is a=4.1.

The second side given is b=2.5.

The expression for the area of triangle is,

`A=(1)/(2)ab\sin C`

Substitute the given values in the above expression.

`\begin{gathered} 5=(1)/(2)(4.1)(2.5)\text{ sin C} \\ \sin C=0.97561 \\ C=102.7^(\circ) \end{gathered}`

Thus, the value of the angle is 102.7 degrees.