Question

Find the area of triangle ABC.

A. 35.92 units²
B. 43.79 units²
C. 21.39 units²
D. 22.91 units²

Answer 1

Answer:

$\text{C. }21.39\:\mathrm{units^2}$

Step-by-step explanation:

The area of a triangle with sides $a$ and $b$ and angle $\gamma$ between them is given by $A=\frac{1}{2}ab\sin \gamma$.

Therefore, in the given triangle, we want to find two sides with the angle between them given. In this case, the angle between the two sides 7.39 and 9.75 is marked as $36.43^{\circ}$. Assign values:

• $a\implies 7.39$
• $b\implies 9.75$
• $\gamma \implies 36.43^{\circ}$

Substituting these values into our area formula, we get:

$A=\frac{1}{2}\cdot 7.39\cdot 9.75\cdot \sin (36.43)^{\circ},\\A=21.3938371858,\\A\approx \boxed{21.39\:\mathrm{units^2}}$