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

Question

asked Oct 2, 2021 99.8k views

2 Answers

Vinayvasyani · Answer 1 · 2021-10-05T08:27:05+0000

Answer:

$\huge \boxed{\mathrm{146.8 \ units^2 }}$

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.

Nelly Sattari · Answer 2 · 2021-10-08T21:48:13+0000

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°

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