Ex 9.1 Q4 - 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.
Solution:- *AB be the height of the tower
*C be the point of observation
Given,
*Angle of elevation = ∠ACB = 30°
*Distance of point C from foot of
the tower = BC = 30 m
➙ In ∆ABC, ∠ABC = 90°,
∴ tanC =
Opposite side of ∠C
/
Adjacent side of ∠C
∴ tan30° =
AB
/
BC
∴ tan30° =
AB
/
30
{ Given } ∴
1
/
√3
=
AB
/
30
{ ∵ tan30° = 1/√3 } ∴ AB =
30
/
√3
*Multiplying Numerator and Denominator by √3
∴ AB =
30
/
√3
×
√3
/
√3
∴ AB =
30√3
/
3
∴ AB = 10√3
Hence,
The height of the tower is 10√3 m.
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Try This..
✒ From a point on the ground, the angle of elevation of a tree’s top is 40° and the point is 25 m away. Find the height of the tree.
✒ A ladder is placed against a wall such that it makes a 60° angle with the ground. If the foot of the ladder is 5 m away from the wall, find the height at which the ladder touches the wall.
✒ The angle of elevation of the top of a building from a point on the ground is 45°. If the building is 20 m high, find the distance from the point to the building.
❌ Common Mistakes
Confusing angle of elevation with depression:▸ Always look upward from the horizontal for elevation.Incorrect trigonometric ratio:▸ Use tan when you have opposite and adjacent sides.Using wrong angle value:▸ Make sure your calculator is set to degrees, not radians, if you're calculating manually.Forgetting to rationalize the denominator:▸ Teachers often deduct marks for leaving irrational numbers in the denominator.
📝 Related Questions:-
- Ex 9.1 Q1 - 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°.
- Ex 9.1 Q2 - 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.
- Ex 9.1 Q3 - 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 3 m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
- Ex 9.1 Q5 - 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.
- Ex 9.1 Q8 - A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Queries Solved:-
Class 10 Ex 9.1
Ex 9.1 Q4 Class 10
Class 10 Ex 9.1 Q4
Class 10 Chap 9 Ex 9.1 Q4
Class 10 Some Applications Of Trigonometry
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