Angle of Elevation and Depression (tops of towers)

pajbo

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Oct 17, 2017
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Hey, I´m stuck on thess tasks for almost an hour and I don´t know how to solve it.

1) The angle of elevation of the top if a tower is 38° from a Point A due south of it. The angle of elevation of the top of the tower from another point B, due east of the tower is 29°. Find the height of the tower if the distance AB is 50m.

2) An observer at the top of a tower of height 15m sees a man due west of him at an angle of depression 31°. He sees another man due south at an angle of depression 17°. Find the distance between the men.

Thank you so much.
 
I´m stuck on [these] tasks for almost an hour …

1) The angle of elevation of the top if a tower is 38° from a Point A due south of it. The angle of elevation of the top of the tower from another point B, due east of the tower is 29°. Find the height of the tower if the distance AB is 50m.

2) An observer at the top of a tower of height 15m sees a man due west of him at an angle of depression 31°. He sees another man due south at an angle of depression 17°. Find the distance between the men.
Please show what you tried, on exercise (1). :cool:
 
I got this:

tan39 * (sin (alpha)*50)= tan 28
You did not show where this came from. I might be able to decipher what your 'alpha' represents, if I spent time experimenting. I'm sorry, but I don't have time to guess (at the moment).

Also, it looks like you transposed some digits; the given angle measurements are 38° and 29°.


In the following diagram, the tower has height h; its base is at O. The distance from O to A is a, and the distance from O to B is b. Triangle AOB is a right triangle.

hTower.jpg

There are three variables (a, b, h).

Try to write three equations (think: right-triangle trigonometric definitions and Pythagorean Theorem). Solve for h, using the substitution method. :cool:
 
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Were you able to finish this exercise? :cool:

Here are three equations that I had in mind:

tan(38°) = h/a

tan(29°) = h/b

a^2 + b^2 = 50^2
 
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