Question

from the top tower 30 m height a man is observing the base of a tree at an angle of depression measuring 30 degree. find the distance between tree and tower.

Answer 1

Answer:

tan30=oposite/adjucent side

1/1.732=30/adjectent side

adjectent side=30*1.732

adjecent side=51.96m.

Answer 2

The distance between tree and tower is 30√3 m

Step-by-step explanation:

Given that

• Height of tower (H) = 30 m

       Distance between from base of tree to tower = B = Unknown

       Angle of depression (∠α) = 30°

• We know that

        Angle of elevation = Angle of depression

        Angle of elevation = ∠α

        Angle of elevation =  30°

• Now from trigonometric relation

        $\mathbf{\tan \alpha =\frac{H}{B}}$

        $\mathbf{\tan 30 =\frac{30}{B}}$    

        $\mathbf{\frac{1}{\sqrt{3}}=\frac{30}{B}}$

         So

         B = 30√3 m = This is the distance between tree and tower.