Posted by **Faw** on Thursday, August 7, 2014 at 6:33am.

two points A and B 80 ft. apart lie on the same side of a tower and in a horizontal line through its foot. if the angle of elevation of the top of the tower at A is 21 degree and B is 46 degree, find the height of the tower.

- math -
**Reiny**, Thursday, August 7, 2014 at 8:15am
Let P be the foot of the tower, and h be the height of the tower

let AP = x , then BP = 80-x

I see two right-angled triangles

tan21 = h/x ---> h = xtan21

tan46 = h/(80-x) --> h = (80-x)tan46

xtan21 = (80-x)tan46

xtan21 = 80tan46 - xtan46

xtan21 + xtan46 = 80tan46

x(tan21 + tan46) = 80tan46

x = 80tan46/(tan21 + tan46) ----- I have not yet touched a calculator

you do the button pushing to get x

then plug x into

h = xtan21

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