Question

Find the area of the given triangle a = 19, c= 14, B=60°. Round your answer to the nearest tenth. ​

Answer 1

`\huge \boxed{\mathrm{115.2 \ units^2 }}`

Explanation:

We can solve for the area of the triangle when two sides are given and the angle in between the two sides.

`\displaystyle A=\mathrm{(1)/(2)ac \cdot sinB }`

`\displaystyle A=\mathrm{(1)/(2) \cdot 19 \cdot 14 \cdot sin60 }`

`\displaystyle A=\mathrm{(133√(3) )/(2) }`

`\displaystyle A=\mathrm{115.18137870...}`

The area of the triangle is 115.2 units².

Answer 2

Answer: 115.2 units²

Explanation:

Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:

`Area=(1)/(2)ac \sin B`

Given: a = 19, c = 14, B = 60°

`A=(1)/(2)(19)(14) \sin 60^o\\\\.\quad =133\sin 60^o\\\\.\quad =115.2`