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.

The figure contains a triangle. One side is 12 centimeters. A second side is 8 centimeters. The angle between the given sides is 65 degrees.

Answer 1

ASSUMING THE UNKNOWN IS THE HYPOTENUSE

Area=1/2absinx
Area=1/2(8)(12)sin65
Area=39.7cm^2

Answer 2

The area of the triangle is 43.5 cm².

Explanation:

Since, the area of a triangle is,

`A=(1)/(2)* s_1* s_2* sin \theta`

Where,
`s_1` and
`s_2` are adjacent sides and
`\theta` is the included angle of these sides,

Given,

`s_1=12\text{ cm}`

`s_2=8\text{ cm}`

`\theta = 65^(\circ)`

Hence, the area of the given triangle is,

`A=(1)/(2)* 12* 8* sin 65^(\circ)`

`=(96* 0.90630778703)/(2)`

`=\frac{87.0055475555}2}=43.5027737778\approx 43.5\text{ square cm}`