Question

find the area of this triangle.
10 m
55°
12 m
? m²
round your answer to the nearest hundredth.

Explanation:

Step1: Recall the formula for the area of a triangle with two sides and included angle

The formula for the area \( A \) of a triangle when two sides \( a \) and \( b \) and the included angle \( C \) are known is \( A=\frac{1}{2}ab\sin C \).
Here, \( a = 12\space m \), \( b = 10\space m \), and \( C = 55^{\circ} \).

Step2: Substitute the values into the formula

Substitute \( a = 12 \), \( b = 10 \), and \( C = 55^{\circ} \) into the formula:
\( A=\frac{1}{2}\times12\times10\times\sin(55^{\circ}) \)
First, calculate \( \frac{1}{2}\times12\times10 = 60 \).
Then, find \( \sin(55^{\circ}) \approx 0.8192 \).
Multiply these results: \( A = 60\times0.8192 = 49.152 \).

Step3: Round to the nearest hundredth

Rounding \( 49.152 \) to the nearest hundredth gives \( 49.15 \).

Answer:

49.15