Question

find the area of the triangle given a = 14, c=21, and B=87°. Round your answer to the nearest tenth.​

Answer 1

`\huge \boxed{\mathrm{146.8 \ 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 14 \cdot 21 \cdot sin87 }`

`\displaystyle A=\mathrm{147 \cdot sin87 }`

`\displaystyle A=\mathrm{146.79854160...}`

The area of the triangle is 146.8 units².

Answer 2

Answer: 143.8 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 = 14, c = 21, B = 87°

`Area=(1)/(2)(14)(21) \sin 87^o\\\\.\qquad =147\sin 87^o\\\\.\qquad =143.8`