Find the area of the triangle given a = 24, b=40, and C= 55°. Round your answer to the nearest tenth.

Question

asked Mar 11, 2021 176k views

2 Answers

Ponds · Answer 1 · 2021-03-12T02:29:52+0000

Answer:

$\huge \boxed{\mathrm{393.2 \ units^2 }}$

Explanation:

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

$\displaystyle A=\mathrm{(1)/(2)ab \cdot sinC }$

$\displaystyle A=\mathrm{(1)/(2) \cdot 24 \cdot 40 \cdot sin55 }$

$\displaystyle A=\mathrm{480 \cdot sin55 }$

$\displaystyle A=\mathrm{393.19298125...}$

The area of the triangle is 393.2 units².

Darko Miletic · Answer 2 · 2021-03-18T07:08:31+0000

Answer: 393.2 units²

Explanation:

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

$A=(1)/(2)ab \sin C$

Given: a = 24, b = 40, C = 55°

$A=(1)/(2)(24)(40) \sin 55^o\\\\.\quad =480\sin 55^o\\\\.\quad =393.2$