Jay is 120 meters from the base of a building and Mary is 40 meters from the base of the building. Jay's angle of elevation when looking at the top of the building is X and Mary's is 2X. What is the height of the building?

Tutors, sign in to answer this question.

tangent=opposite/adjacent, H=height of building

tan(x)=H/120

tan(2x)=H/40

120tan(x)=H

40tan(2x)=H

120tan(x)=40tan(2x)

3tan(x)=tan(2x)

tan(2x)=3tan(x)

tan(2x)=2tan(x)/[1-tan^2(x)]

2tan(x)/[1-tan^2(x)]=3tan(x)

2tan(x)=3tan(x)[1-tan^2(x)]

2=3[1-tan^2(x)]

2/3=1-tan^2(x)

-1/3=-tan^2(x)

1/3=tan^2(x)

find the square root of 1/3

square root of 1/3=0.57735

tan of what angle is 0.57735 from the table of tangents ?

the angle x=30 degrees

tan(30)=H/120

120*0.57735=69.28 meters

2x=60 degrees

tan(60)=H/40

tan(60)=1.7321

40*1.7321=69.28 meters

Use the definition of tangent (opposite/adjacent):

From Jay's point of view, tan (X) = h/120

From Mary's point of view, tan (2X) = h/40

Divide the two equations:

tan(2X)/tan(X) = (h/40)/(h/120) = 3

tan(2X) = 3 tan(X)

Use the double-angle formula

tan(2X) = 2 tan(X) /(1 - tan²(X) )

Get

2 tan(X) /(1 - tan²(X) ) = 3 tan(X)

2 = 3 (1 - tan²(X) )

tan²(X) = 1/3

X= 30°

Therefore,

h=120 tan (30°) ≈ 69 meters

is the height.

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.