Ayres rock is a sacred place for aborigines of the western desert of Australia. Charlie uses a serving device to measure the angle of elevation to the top of th

Question

Ayres rock is a sacred place for aborigines of the western desert of Australia. Charlie uses a serving device to measure the angle of elevation to the top of the rock to be 11.5°. he walks half a mile 5280 feet closer and measures the angle of elevation to be 23.9°. how high is Ayers rock in feet?

Answer 1

when angle of elevation is 11.5 serving device is at distance=x feet

when a angle of elevation is 23.9 serving device is at distance= x- (1/2 mile5280 feet)

                                                                                        =x- (2640+5280)

                                                                                         = x-7920 feet

 

h=height of Ayears rock

 

tan 11.5 = h/x         -------- equation 1

 

tan 23.9= h/x-7920   -------equation 2

 

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tan 11.5 = h/x

 

x=h/tan11.5

 

x=h/0.2036

 

-----------------------------------------------------------------------

 

tan 23.9= h/x-7920

           =h/(h/0.2036)-7920

 

after calculating this

h=0.0395 feet