MHB How Tall are Buildings A and B Using Trigonometry?

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Buildings A and B are 35 meters apart, with Building A's height calculated using the angle of depression to Building B's base at 34°, resulting in a height of 24 meters. The height of Building B is determined using the angle of elevation from Building A's roof at 24°, yielding a height of 16 meters. Therefore, Building B's total height is 40 meters. The calculations are confirmed to be correct, but it is advised to retain decimal precision to minimize rounding errors. The discussion emphasizes the importance of accuracy in trigonometric calculations.
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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.
 
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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.
 
anemone said:
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.
 
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