# Right Angle Trigonometry

1. Dec 14, 2014

### ciubba

Problem was initially posted in a technical math section, so is missing the homework template.
From a position 150 ft above the ground, an observer in a building measures angles of depression of 12° and 34° to the top and bottom, respectively, of a smaller building, as in the picture on the right. Use this to find the height h of the smaller building.

I have found that the angle between the observer and the ground is 56°; however, when I use the tangent function to get the distance between the smaller building and the observer [150 tan(56)] I get the wrong answer and I do not understand why. The only solutions to this problem that I have found involve the law of sines, which has not been covered yet. If I knew the distance between the observer and the smaller building (let's call it x), then I would be able to construct a right triangle from the observing to above the smaller building, where the triangle would have acute angles 78 and 12 and a leg of length x; however, I would not know how to proceed from there.

My questions are: why can I not use [150 tan(56)] to calculate x, how do I calculate x, and how do I find h from the triangle with leg x and angles 78 and 12.

Last edited by a moderator: Dec 15, 2014
2. Dec 14, 2014

### Staff: Mentor

A drawing would be very helpful.

One thing I need to ask - is your calculator in degree mode?

3. Dec 14, 2014

### ciubba

I did my best to draw it, and yes, my calculator is in degree mode. I used variables to represent any quantity that wasn't explicitly given to me by the problem. By the complement rule, I think theta is 56°; however, I get the wrong answer for x when I do [150 tan(56)]. It is apparently solvable without the law of sines as the book has not covered that idea yet.

I believe that A is 90° and that B is 78°. I want to find the variable "h," which is the height of the small building.

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4. Dec 15, 2014

### Staff: Mentor

Your equation of x = 150 tan(56°) is fine. I did it another way, but the two ways are equivalent. All you need is another equation that involves x and h.

In your drawing, extend the line segment of length h all the way to the top so that you have a rectangle that is 150' by x'. Using the 34° you can use the dimensions of the triangle whose acute angle is 34° - that's your second equation. You don't need the Law of Sines or the Law of Cosines - just some ordinary right triangle trig.

BTW, this is a homework problem, so I am moving it to the Homework & Coursework sections, which is where problems of this sort should be posted.

5. Dec 15, 2014

### ciubba

Oh, it looks like I forgot to subtract h from 150! The answer is then 103. Thank you for the advice!