Question

Trigonometry help? 

Answer 1

(1)

The distance between the surveyor and the tree is 18 m .

The angle of elevation is 47° .

Let the height of the tree is x .

From the figure tan ϴ = opposite side length / adjacent side length 

                      tan 47 =  x / 18     

                ⇒ x = 18 * tan 47  = 18 * (1.0723)= 19.3026 m

So the height of the tree is 19.3026 m .

Answer 2

(2)

The length of the shadow of building  is 34 m .

The height of the building is  56 m .

Let the angle of elevation is ϴ .

From the figure tan ϴ = opposite side length / adjacent side length 

                      tan ϴ =  56 / 34  = 1.647   

                ⇒ ϴ = arctan (1.647 ) = 58.736°

So the angle of elevation is ϴ = 58.736°  .