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lawyer [7]
3 years ago
10

Adam and Kevin are standing 35 metres apart, on opposite sides of a flagpole. From Adam’s position, the angle of elevation of th

e top of the flagpole is 36°. From Kevin’s position, the angle of elevation is 50°. How high is the flagpole?
Mathematics
1 answer:
Nadusha1986 [10]3 years ago
4 0
1. Lets' call:

 H: The height of the flagpole.
 x: The distance f<span>rom Adam’s position to the flagpole.
</span> y: The distance from Kevin’s position to the flagpole.

 2. So, we have:

 Tan(36°)=H/x ⇒ x=H/Tan(36°)    (i)

 Tan(50°)=H/y ⇒ y=H/Tan(50°)    (ii)

 3. We know that <span>Adam and Kevin are standing 35 meters apart. Then:
</span>
 x+y=35    (iii)

 4. Let's substitute (i) and (ii) in (iii):

 x+y=35
 H/Tan(36°)+H/Tan(50°)=35
 H(1/Tan(36°)+1/Tan(50°)=35

 5. When we clear "H", we obtain:

 H=35/(1/Tan(36°)+1/Tan(50°))
 H=15.79 meters

 How high is the flagpole?  

 The answer is: 15.79 meters
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