The Angle of Elevation and depression

      

The foot of a ladder is 6m from the base of an electric pole, and the top of the ladder rests against the pole at a point 8m above the ground. How long is the ladder?

                                             Solution

                                  

                                                           

 

             Let the length of the ladder be = x

X²  = 6² + 8²   ( Pythagoras’ theorem)

X² = 36 + 64

X²  = 100

X =√100  

X = 10

^{Question source WAEC.}

          From the top of a vertical cliff 20m high, a boat at sea can be sighted 75m away and on the same horizontal position as the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.

 

                     

                                                                               

 

                                                                                              

                                                         

SOH CAH TOA 

Tan θ = 20/70

Tan θ = 0.2667

Θ= 14.9 = 15⁰

^{Question source WACE}                        

From a point 14√3 metres away from a tree is 30⁰,  if the man measures this angle of elevation from a point 2 metres above the ground, how high is the tree?      

                            Solution

 

 

Tan 30 = h/14√3

√3/3 =h/14√3

3h = 14√3 x √3

3h = 14 x 3

3h = 42

H =42/3 = 14

The actual height of the tree is 14+2 = 16

     ^{Question credited to JAMB}