Expert: Sherman D. - 12/16/2006

Question
hey, again can you help with these two last questions i got them incorrect also must show work thanks for you all your help!

1). A man standing on top of a building sees an automobile on a street below him. The angle of depression is 36°22'. If his eye is 550ft above the level of the automobile,how far is the automobile from him?

2).When the sun's angle of elevation is 30° the shadow of a post is 6 ft longer than when the angle is 45°. Find the height of the post.

Answer
1.)
If you are talking about him specifically and not from the building he is standing on, then

cos(36°22') = 550/x
x = 550/cos(36°22')
x = about 683.03ft

But if you are talking about from the building, then

tan(90° - 36°22') = 550/y
tan(53°38') = 550/y
y = 550/tan(53°38)
y = 405ft

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2.)

tan(30) = x/y
y = x/tan(30)

tan(45) = (x + 6)/y
y = (x + 6)/tan(45)

Keep in mind that the sun remains at the same height

x/tan(30) = (x + 6)/tan(45)
tan(30)(x + 6) = tan(45)x
(sqrt(3)/3)(x + 6) = 1(x)
(sqrt(3)/3)(x + 6) = x
sqrt(3)(x + 6) = 3x
x + 6 = (3/sqrt(3))x
x + 6 = sqrt(3)x
x - sqrt(3)x = -6
x(1 - sqrt(3)) = -6
x = -6/(1 - sqrt(3))
x = about 8.196 ft long

ANS : about 8 ft tall

It helps to draw it out.

So that i didn't confused, i drew 2 different right triangles.