Question

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.

Answer 1

Draw it

Answer 2

i have it drawn out already

Answer 3

Do our drawings look the same?

Answer 4

yes

Answer 5

So do you know how we might possibly go about solving this?

Answer 6

Hmm, have you heard of something called Law of Sines?

Answer 7

not really and no that doesnt sound familiar

Answer 8

Looks like this

\[\frac{ a}{ \sin A} = \frac{ b }{ \sin B } = \frac{ c }{ \sin C }\]

Answer 9

Ever used sine before?

Answer 10

kinda, this is still pretty new to me

Answer 11

Basically, a, b, and c, are all side lengths,

A, B, and C are angles

What you want to do, is get three knowns, to solve for one unknown. For example:
-In order to solve for an unknown angle, I need at least one other angle and two side lengths.
-In order to solve for an unknown side, I need at least one other side and two angles.

Answer 12

In this problem, do you know what we are given?

Answer 13

what given.. would it be the angle 74, and the base 34?

Answer 14

Correct. And what are we solving for?

Answer 15

the side length.. which is the height of the building?

Answer 16

Yes. So our side length is our unknown, and then we have a defined side length and a defined angle. What must we need?

Answer 17

In order to solve for this unknown side length, which is the height of the building?

Answer 18

the hypnotuse?.. idk how to spell it

Answer 19

Hmm, no. When we want to solve for an unknown side length, what do we need?

Answer 20

I posted it earlier :)

Answer 21

the sine?

Answer 22

In order to solve for an unknown side length, we need a known side length and two angles.

What's important about these measurements is that they must correlate to each other.

So,

\[\frac{ a}{ \sin A} = \frac{ b}{ \sin B }\]

We are given:

\[\frac{ 34}{ \sin A} = \frac{ b}{ \sin 74 }\]

We have two unknowns. We are solving for b, the side length opposite to angle 74 (the angle of elevation). So how do we get the measurement of angle A?

Answer 23

If you don't know how, just tell me and I can show you.

Answer 24

im not really sure how

Answer 25

Do you know the sum of all the angles in a triangle?

Answer 26

its 180 isnt it

Answer 27

Yes.

So this is a right triangle. That's because the ground is perpendicular to the side of a building (they form a 90 degree angle).

This means that we can solve for the last angle, since we know the first two.

\[180 - 90 - 74 = ?\]

Answer 28

so angle A would be 16?

Answer 29

Correct

Answer 30

So now we have

\[\frac{ 34 }{ \sin 16 } = \frac{ b }{ \sin 16}\]

Answer 31

We can solve for b

\ \

Answer 32

For some odd reason that isn't showing up ._.

Answer 33

If you type that into a calculator, you should ger 118.6

Answer 34

So your final answer should be 118.6ft

Answer 35

ohh ok, that seemed alot easier than what i was making it. so i just put that in for my work?

Answer 36

Yeah. The main focus is Law of Sines, but first finding the proper measurements for it. Requires knowledge of what angles/sides you need, and that the sum of all angles in a triangle is 180.

Answer 37

kk thx so so much for all ur help