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When the sun is shining at a 62º angle of elevation, a flagpole forms a shadow of length x feet. Later, the sun shines at an angle of 48º, and the shadow is 16 feet longer than before.

 

A. Write two expressions for the height h of the flagpole in terms of x.

B. How tall is the flagpole?

 Feb 19, 2016
 #1
avatar+23245 
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A)

Let h represent the height of the flagpole. 

When the angle of elevation is 62°, tan(62°) = h/x   --->   x  =  h/tan(62°)

When the angle of elevation is 48°, tan(48°) = h/(x+16)   --->   x + 16  =  h/tan(48°)   --->   x  =  h/tan(48°) - 16

B)

Since there are two equations for x, they can be set equal to each other.

h/tan(62°)  =  h/tan(48°) - 16

h/1.8807  =  h/1.1106 - 16           (since 1/1.8807 = 0.5317  and  1/1.1106 = 0.9904)  --->

0.5317h  =  0.9004h - 16             (subtract 0.9004 from both sides)  --->

- 0.4587h  =  -16                           (divide both sides by -0.4587)  --->

h  =  35 feet (approximately)

 Feb 19, 2016
 #2
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Thank you!

Olivia3.141592654  Feb 19, 2016

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