Question

What is the area of this triangle?Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. cm²The figure contains a triangle. One side is 11 centimeters. A second side is 9 centimeters. The angle between the given sides is 63 degrees.

Answer 1

The figure contains a triangle. One side is 11 centimeters. A second side is 9 centimeters

To determine the area of the triangle

To find : Area of triangle .

Solution : We have given two sides to triangle = 11 cm , 9 cm .

Angle between two sides = 65 degree.

Where , a and b are two sides and C is angle between them .

Now, plugging the values

`\begin{gathered} \theta=63 \\ a=11cm \\ b=9cm \end{gathered}`

`\begin{gathered} \text{Area of the triangle = }(1)/(2)ab\sin \theta \\ A=(1)/(2)ab\sin \theta \\ A=(1)/(2)(11)(9)\sin 63 \\ A=(99)/(2)(0.8910) \\ A=49.5(0.8910) \\ A=44.104 \\ A\approx44.1\text{ (nearest tenth)} \end{gathered}`

Therefore the area of this triangle = 44.1cm² ( nearest tenth)