We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
472
1
avatar+129 

From a point on a line from the base of the Washington Monument, the angle of elevation to the top of the monument is 42.0°. From a point 100 feet away from on the same line, the angle to the top is 37.8°. Find the height, to the nearest foot, of the Washington Monument.

 May 4, 2018
 #1
avatar+101369 
+1

Let the height of the monument  = h

Let the distance from the base of the monument to a point directly under the apex  = x

 

So   we have these equations

 

tan(42)  =  h / x     rearrange as

 

x  =   h / tan (42)      (1)

 

We also have

 

tan (37.8)  =  h / (100 + x)

 

(100 + x) tan (37.8)   = h

 

100*tan(37.8)  + x *tan (37.8)  =  h     (2)

 

Sub  (1)  into (2)

 

100* tan(37.8)  + (h /tan(42)* tan (37.8)  = h

 

100* tan(37.8)  =  h  -  h [ tan (37.8) / tan(42) ]

 

100* tan (37.8)  =  h  [  1  - tan(37.8)/tan(42) ]

 

h  =     [ 100 * tan (37.8) ]  /  [  1 - tan(37.8)/tan(42) ] ≈  560 ft

 

 

cool cool cool

 May 4, 2018

14 Online Users

avatar
avatar