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Simon bought a new shop and wants to order a new sign for the roof of the building. From point P, he finds the angle of elevation of the roof, from ground level, to be 31º and the angle of elevation of the top of the sign to be 42º. If point P is 8 meters from the building, how tall is the sign to the nearest tenth of a meter?

 Jan 12, 2024
 #1
avatar+129185 
+1

Height of sign  = Height from ground to top of sign  -  Height from ground to roof

 

                                             (a)                                -            (b)

 

                             tan (42°) =  a / 8                             tan (31°) = b / 8

 

    a  -  b   =  

 

8   tan ( 42°)  -  8 tan (31°)  =

 

8 ( tan (42° ) - tan (31°)  ≈  2.4 m

 

 

cool cool cool

 Jan 12, 2024

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