Solve the problem.
-A painter is going to apply a special coating to a triangular metal plate on a new building. Two sides measure are $10.0 \mathrm {~m}$ and $7.1 \mathrm {~m}$. She knows that the angle between these sides is $37.2 ^ { \circ }$. What is the area of the surface she plans to cover with the coating? Round to the nearest square meter.
A) $19 \mathrm {~m} ^ { 2 }$
B) $30 \mathrm {~m} ^ { 2 }$
C) $28 m ^ { 2 }$
D) $21 \mathrm {~m} ^ { 2 }$

Question

Quizplus · Accepted Answer

The area of a triangle given two sides and the included angle can be calculated using the formula: $ \frac{1}{2}ab\sin(C) $, where $a$ and $b$ are the sides and $C$ is the included angle. Here, $a = 10.0 \, \mathrm{m}$, $b = 7.1 \, \mathrm{m}$, and $C = 37.2^\circ$. Plugging these values into the formula gives $ \frac{1}{2} \times 10.0 \times 7.1 \times \sin(37.2^\circ) \approx 21 \, \mathrm{m}^2 $, rounding to the nearest square meter.

Solve the Problem 10.0 m10.0 \mathrm {~m}10.0 m And 7.1 m7.1 \mathrm {~m}7.1 m She Knows That the Angle Between These Sides Is

Solve the Problem $10.0 \mathrm {~m}$ And $7.1 \mathrm {~m}$ She Knows That the Angle Between These Sides Is