Let AC be the rope whose length is 20 m, and AB be the vertical pole of height h m and the angle of elevation of A at point C on the ground is 30°.


Fig. 9.11
i.e.,    ∠ACB = 30°
In right triangle ABC, we have

Hence, the height of the pole is 10 m.

Let BD be the tree broken at point C such that the broken part CD takes the position CA and strikes the ground at A. It is given that AB = 8 m and ∠BAC = 30°.
Let BC = x metres and CD = CA = y metres
In right triangle ABC, we have



Now, height of the tree

Hence, the height of the tree 

Case I :

Calculation of length of the slide below 5 years. Fig. (a)
Let AC be the slide of length l m and height of the slide AB of height 1.5 m. It is given that slide is inclimed at an angle of 30°.
i.e.,    ∠ACB = 30°
In right triangle ABC, we have

Hence, the length of the slide for below 5 years is 3 m

Case II :

Calculation of the length of slide for elder children. Fig. (b)
Let DF be the slide of length m metres and DE be the height of the top of slide of height 3 m. It is given that slide is inclined at an angle of 60°.
i.e.,    ∠DFE = 60°
In right triangle DEF, we have

Hence, the length of the slide for elder children is 

Let A be the top and B be the foot of the tower AB, of height h metre. C be the point which is 30 m away from the tower i.e. BC = 30 m.
Now,
AB = h m
BC = 30 m
and    ∠ACB = 30°
In right triangle ABC, we have



Hence, the height of the tower is