Please help. Show work so I can understand. Thanks 7- [55.7] Find the height in

Question

Please help. Show work so I can understand. Thanks

7- [55.7] Find the height in feet of both a tall building and a radio tower which is itself built on the very top of the tall building, given that you are standing at ground level 150 feet horizontally from the base of the tall building and the angle of elevation from you to the bottom of the radio tower is 75 degrees (i.e., the angle from you to the top of the building) and the angle of elevation from you to the top of the radio tower is 77 degrees. [Hint: Remember to draw a picture!] Tell the height in feet only of the tall building, not including the height of the tower on top of the building, to the nearest foot. a) Tell the height in feet only of the tower itself (which is, of course, situated on top of the building), not the building and the tower together, to the nearest foot. b)

Explanation / Answer

7)  

let the height of the tallbuilding = h feet

and height of radio tower = x feet

applying tan rule

tan 75 = h/ 150

h = 150 tan 75

h = 560

height of the building = 560 feet

b) applying tan rule on another triangle

tan 77 = ( h + x) / 150

h + x = tan 77 * 150

h + x = 649.72

x = 649.72 - 560

x = 90

height of the tower = 90 feet

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