A man 5 ft 9 in tall stands on a sidewalk that slopes down at a constant angle.  A vertical street lamp directly behind him causes his shadow to be 25 ft long.  The angle of depression from the top of the man to the tip of his shadow is 31o .  Find the angle (alpha) that the sidewalk makes with the horizontal.

Question
Asked Nov 7, 2019

A man 5 ft 9 in tall stands on a sidewalk that slopes down at a constant angle.  A vertical street lamp directly behind him causes his shadow to be 25 ft long.  The angle of depression from the top of the man to the tip of his shadow is 31o .  Find the angle (alpha) that the sidewalk makes with the horizontal.

            

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Step 1

Given that

A man 5 ft 9 in tall stands on a sidewalk that slopes down at a constant angle.  A vertical streetlamp directly behind him causes his shadow to be 25 ft long. The angle of depression from the top of the man to the tip of his shadow is 31o as shown

pole
| 31
5.75
shadow
25
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pole | 31 5.75 shadow 25

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Step 2

To find out the angle alpha

Step 3
First of all 5ft 9 in= 5.75 ft
From the figure
ZBDC =
sum of angle of a triangle=180
ZCBD= (90°-a)
then
ZABD= 180°-(90-a)
LABD=(90°+a)
ZBAD=90°-31
ZBAD= 59°
Then
LADB = 180°- (59 +(90°+a))
sum of angle of a triangle=180°
LADB= (31°-a)
help_outline

Image Transcriptionclose

First of all 5ft 9 in= 5.75 ft From the figure ZBDC = sum of angle of a triangle=180 ZCBD= (90°-a) then ZABD= 180°-(90-a) LABD=(90°+a) ZBAD=90°-31 ZBAD= 59° Then LADB = 180°- (59 +(90°+a)) sum of angle of a triangle=180° LADB= (31°-a)

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