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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 :

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,

[tex]A=\frac{1}{2}ab\sin C[/tex]

Substitute the given values in the above expression.

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

Thus, the value of the angle is 102.7 degrees.

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