Trigonometry Height and Distance

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #31

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow from the same point in water of lake is 60°. Find the height of the cloud from the surface of water.
Ans: 120 m
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Question No: #32

If the angle of elevation of a cloud from a point `h` meters above a lake is `\alpha` and the angle of depression of its reflection in the lake is `\beta`, prove that the distance of the cloud from the point of observation is `\frac{2h sec \alpha}{tan \beta - tan \alpha`

Question No: #33

The angle of elevation of the hilltop from the foot of a hill is 45°. Climbing up 2 km along the bottom at a 30° angle to the hill, the top of the hill can be seen at an angle of 60°. Find the height of the mountain.
Ans: `(\sqrt{3}+1)` km
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Question No: #34

A ladder rests against a vertical wall at an inclination `\alpha` to the horizontal. Its foot is pulled away from the wall through a distance `p` unit so that its upper end slides `q` unit down the wall and then ladder make an angle `\beta` to the horizontal. Show that, `p/q = \frac{cos \beta - cos \alpha}{sin \alpha - sin \beta`