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 $10.7 \mathrm {~m}$ and $6.4 \mathrm {~m}$. She knows that the angle between these sides is $25.3 ^ { \circ }$. What is the area of the surface she plans to cover with the coating? Round to the nearest square meter.
A) $13 \mathrm {~m} ^ { 2 }$
B) $31 \mathrm {~m} ^ { 2 }$
C) $15 \mathrm {~m} ^ { 2 }$
D) $33 \mathrm {~m} ^ { 2 }$

Question

Quizplus · Accepted Answer

The area of a triangle is given by the formula $A = \frac { 1 } { 2 } b h$, where $b$ is the length of the base and $h$ is the height. In this case, the base is $10.7 \mathrm {~m}$ and the height is the length of the side opposite the $25.3 ^ { \circ }$ angle. To find the height, we can use the sine function:$$\sin 25.3 ^ { \circ } = \frac { h } { 6.4 \mathrm {~m} }$$Solving for $h$, we get:$$h = 6.4 \mathrm {~m} \sin 25.3 ^ { \circ } \approx 2.7 \mathrm {~m}$$Now we can calculate the area of the triangle:$$A = \frac { 1 } { 2 } ( 10.7 \mathrm {~m} ) ( 2.7 \mathrm {~m} ) \approx 14.4 \mathrm {~m} ^ { 2 }$$Rounding to the nearest square meter, we get $15 \mathrm {~m} ^ { 2 }$.

Solve the Problem 10.7 m10.7 \mathrm {~m}10.7 m And 6.4 m6.4 \mathrm {~m}6.4 m She Knows That the Angle Between These Sides Is

Solve the Problem $10.7 \mathrm {~m}$ And $6.4 \mathrm {~m}$ She Knows That the Angle Between These Sides Is