Math / Geometry

QuestionFind the area of this triangle. Round to the nearest tenth.

Studdy Solution

STEP 1

1. We are given a triangle with two sides and the included angle.
2. The sides measure 8 meters and 12 meters.
3. The included angle is $62^\circ$ .
4. We need to find the area of the triangle and round it to the nearest tenth.

STEP 2

1. Use the formula for the area of a triangle when two sides and the included angle are known.
2. Calculate the area using the formula.
3. Round the result to the nearest tenth.

STEP 3

The formula for the area of a triangle when two sides and the included angle are known is:
$\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)$
where $a$ and $b$ are the lengths of the two sides, and $C$ is the included angle.

STEP 4

Substitute the given values into the formula:
$a = 8 \, \text{meters}, \, b = 12 \, \text{meters}, \, C = 62^\circ$
$\text{Area} = \frac{1}{2} \times 8 \times 12 \times \sin(62^\circ)$

STEP 5

Calculate $\sin(62^\circ)$ using a calculator:
$\sin(62^\circ) \approx 0.8829$

STEP 6

Substitute $\sin(62^\circ) \approx 0.8829$ into the area formula and calculate:
$\text{Area} = \frac{1}{2} \times 8 \times 12 \times 0.8829$
$\text{Area} = 48 \times 0.8829$
$\text{Area} \approx 42.3792$

STEP 7

Round the calculated area to the nearest tenth:
$\text{Area} \approx 42.4$
The area of the triangle, rounded to the nearest tenth, is:
$\boxed{42.4} \, \text{square meters}$

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