Posted by **Jennifer** on Wednesday, November 11, 2009 at 12:48pm.

From a point A on the ground, the angle of elevation to the top of a tall building is 24.1 degrees. From a point B, which is 600 ft closer to the building, the angle of elevation is measured to be 30.2 degrees. Find the height of the building. PLEASE HELP ME!

- Trig -
**drwls**, Wednesday, November 11, 2009 at 1:15pm
Get out a piece of paper and draw the situation. You have two right triangles. Each have two points that are the same (the top and bottom of the bulding), but the third points (where the observer is located) are different. Let H be the height of the building, in feet. Point A is X ft away and point B is A - 600 feet away.

Solve those two simultaneous equations:

H/X = tan 24.1

H/(600-X) = tan 30.2

As a first step in solving them, you can solve for X first, using

(600-X)/X = tan 30.2/tan 24.1 = 1.3011

(I used a calculator for that)

Rewrite as

780.67 = 2.3011 X

X = 339.3 ft

Now use either of the first two equations to solve for H.

- Trig -
**Reiny**, Wednesday, November 11, 2009 at 1:45pm
or

look at the non-right-angles triangle, with its top angle at the top of the building.

That top angle can be easily found to be 6.1 degrees. We can find the side coming up from the 30.2 degree angle, call it y

by sine law

y/sin24.1 = 600/sin6.1

y = 2305.56

then in the small right-angled triangle

sin 30.2 = H/y

H = 2305.56sin30.2

= 1159.74

## Answer This Question

## Related Questions

- Pre-Calculus - 1.The angle of elevation to top of a building from a point on the...
- Trig - The angle of elevation to the top of a building from a point on the ...
- Precalculus - To estimate the height of a building, two students find the angle ...
- TRIG Help help help test tommarow - A TV tower stands on top of the Empire State...
- Math- Pre calc - A 60 foot antenna stands on top of a building. From a point on ...
- Pre-Cal/Trig - Explain how to solve the following question. Surveying: From a ...
- mathd - From point A,the angle of elevation to the top of a tall building is 20 ...
- Trig - A 60-foot flagpole stands on top of a building. From a point on the ...
- trig - a building 60 feet high. from a distance at point A on the ground, the ...
- College Trigonometry - From a point 200 yards from the foot of a building, the ...

More Related Questions