Question

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

Answer 1

Answer:   393.2 units²

Step-by-step explanation:

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

$A=\dfrac{1}{2}ab \sin C$

Given: a = 24, b = 40, C = 55°

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

Answer 2

Answer:

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

Step-by-step explanation:

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

$\displaystyle A=\mathrm{\frac{1}{2}ab \cdot sinC }$

$\displaystyle A=\mathrm{\frac{1}{2} \cdot 24 \cdot 40 \cdot sin55 }$

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

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

The area of the triangle is 393.2 units².