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Question

a surveyor measures the angle of elevation to the top of a building to be 70*. the surveyor then walks to 50ft farther tfrom the base of the tower and measures the angle of elevation to be 50*. the surveyor's angle-measuring device is 5.5

Answer 1

h= the height of the building
x= the distance between surveyor and building
tan 70= h/x...............>h=x.tan 70
tan 50=h/(x+50).......>h=(x+50).tan 50
....>x.tan 70=(x+50)tan 50
tan 70=2.75
tan 50=1.19
....> 2.75x=(x+50)1.19
>>2.75x=1.19x+59.5
>>1.56x=59.5
>x=38.14
h=x tan70
>h=(38.14)(1.19)
>h=45.38 feet

Answer 2

We have 2 right triangles to work with, one with 70 deg to the top of the building and the other with 50 deg to the top of the building.

We will start with the 70 deg to determine the hypotenuse of the 50 deg.

Using sine law:

sine 20 deg/50 = sine 50/(hyp of 70 deg triangle)

hyp of 70 deg triangle = 111.988 ft

Now we have the hypotenuse of the 70 deg rt triangle 111.988 ft.

Now we work with the 70 deg triangle to solve.

Sin A = side opposite / hypotenuse

sine 70 deg = (building height -5.5)/111.988

building height - 5.5 =105.23

building height = 110.73 ft.

Answer 3

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