Question

find the area of the triangle abc.
a = 12.6 m b = 5.8 m c = 10.2°
what is the area of the triangle?
□ m²
(simplify your answer. type an integer or decimal rounded to the nearest tenth

Explanation:

Step1: Use the area formula for SAS triangle

The formula is $\text{Area} = \frac{1}{2}ab\sin C$, where $a=12.6$, $b=5.8$, $C=10.2^\circ$.

Step2: Calculate the product of a and b

$12.6 \times 5.8 = 73.08$

Step3: Multiply by 1/2

$\frac{1}{2} \times 73.08 = 36.54$

Step4: Calculate $\sin 10.2^\circ$

$\sin 10.2^\circ \approx 0.1771$

Step5: Compute the final area

$36.54 \times 0.1771 \approx 6.47$ (rounded to nearest tenth is 6.5)

Answer:

6.5