The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
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 
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
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 
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
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 
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° (see Fig. 9.11)
Fig. 9.11
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.
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
Let BC be the horizontal ground, and let A be the position of the kite which is at a height of 60 m. i.e., AB = 60 m.
It is given that
∠ACB = 60°
Now, in right triangle ABC, we have
Hence, the length of string is 
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