How Tall are Buildings A and B Using Trigonometry?

[xyz_1965]

Buildings A and B are across the street from each other, 35m apart. From a point on the roof of Building A, the angle of elevation to the top of Building B is 24°, and the angle of depression of the base of Building B is 34°. How tall is each building?

Let x = height of building A.

tan(34°) = x/35

tan(34°)(35) = x

23.61 m = x

I will round off to the nearest ones to get 24 m = x.

Let y = height of building B.

tan(24°) = y/35

tan(24°)(35) = y

15.6 = y

I will round to the nearest ones to get 16 m = y.

Building A is 24 meters tall.
Building B is (24 + 16) or 40 m.

Is any of this right? I have a few more questions to post throughout the day. Thank you.

 

[anemone]

Hi xyz_1965, welcome to MHB!

Yes, your answers to both parts of the problem are correct, well done! Just that if I were you, I would not round the answers to the nearest integer, I would keep both answers correct to 1 or 2 decimal places to avoid round-off error.

 

[xyz_1965]

Hi xyz_1965, welcome to MHB!

Yes, your answers to both parts of the problem are correct, well done! Just that if I were you, I would not round the answers to the nearest integer, I would keep both answers correct to 1 or 2 decimal places to avoid round-off error.

Thanks for the tip.