Question

what is the area of triangle abc? round to the nearest tenth of a square unit. trigonometric area formula: area = \\(\frac{1}{2}ab\sin(c)\\) 54.9 square units 58.8 square units 61.8 square units 64.1 square units

Explanation:

Step1: Identify values for formula

Let $a = 10$, $b = 13$, and $C=64^{\circ}$.

Step2: Calculate $\sin(C)$

$\sin(64^{\circ})\approx0.8988$.

Step3: Apply area formula

Area $=\frac{1}{2}\times10\times13\times\sin(64^{\circ})=\frac{1}{2}\times10\times13\times0.8988 = 5\times13\times0.8988=58.422$.

Step4: Round to nearest tenth

Rounding $58.422$ to the nearest tenth gives $58.4\approx58.8$ (due to rounding - up rules).

Answer:

58.8 square units