Question

SOMEONE HELP ASAPPPPPPP!!! PLEASE

1. A person at ground level measures the angle of elevation to the top of a building to be 74°. If at this point the person is 34 feet away from the base of the building, then how tall is the building?

Please round to the tenths place.
Please show work/steps and provide units with your answer.

2. In right triangle PQR, P and Q are complementary angles. The value of sin Q is
9/
. What is the value of cos P?

A.9/41
B.41/9
C.40/41
D/41/40

Answer 1

Part 1
The distance between the person and the building can be written as:

`x=c\cdot \cos(\theta)`
C would be the line connecting the top of the building and the person(hypotenuse).
The height of the building is:

`h=c\cdot \sin(\theta)`
If we get the c from the first equation and plug in the second one we get:

`h=(x)/(\cos(\theta))\cdot\sin(\theta)=x\cdot \tan(\theta)=32ft\cdot3.45=110.4$ft`
Part 2
If we P and Q are complementary that means that they sum is 90 degrees.
Because of this sin(Q) must be the same as cos(P).
Sum of the angles in any triangle is 180 if we have a right triangle and two complementary angles that means that those two angles have to be 45 degrees. Sin and cos are the same for the 45-degree angle.
I attached the diagram that would make this clear.