Question

find the area of this triangle.
15 m
115°
11 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, \( a = 15 \) m, \( b = 11 \) m, and \( C = 115^\circ \).

Step2: Substitute the values into the formula

Substitute \( a = 15 \), \( b = 11 \), and \( C = 115^\circ \) into the formula:
\( A=\frac{1}{2}\times15\times11\times\sin(115^\circ) \)

First, calculate \( \sin(115^\circ) \). Using a calculator, \( \sin(115^\circ)\approx\sin(90^\circ + 25^\circ)=\cos(25^\circ)\approx0.9063 \) (or directly calculate \( \sin(115^\circ)\approx0.9063 \)).

Then, calculate \( \frac{1}{2}\times15\times11 = \frac{165}{2}=82.5 \).

Now, multiply by \( \sin(115^\circ) \): \( A = 82.5\times0.9063\approx74.77 \) (rounded to the nearest hundredth).

Answer:

\( 74.77 \)