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°.
Solution:-Let,
AB = height of the pole
AC = length of the rope
Given,
Length of rope = AC = 20m
Angle between rope and ground
= ∠ACB = 30°
➙ In ∆ABC, ∠ABC = 90°
∴ sinC =
Opposite side of ∠C
/
Hypotenuse
∴ sin30° =
AB
/
AC
∴ sin30° =
AB
/
20
{Given, AC = 20} ∴
1
/
2
=
AB
/
20
{∵ sin30° = 1/2} ∴ AB =
20
/
2
∴ AB = 10m
Hence,
The height of the pole is 10m.
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Try This..
✒ A boy is looking at the top of a lamp post. If the distance between the boy and the lamp post is 10 m and the angle of elevation is 60°, find the height of the lamp post.
✒ A tree casts a shadow 5 m long when the angle of elevation of the sun is 45°. Find the height of the tree.
✒ A kite is flying at a height of 50 m. If the length of the string is 100 m, find the angle it makes with the horizontal.
✒ A ladder 25 m long is leaning against a wall making an angle of 60° with the ground. Find the height of the wall.
❌ Common Mistakes
Using the wrong trigonometric ratio:▸ Always identify the sides correctly;opposite, adjacent, and hypotenuse;based on the angle.Confusing angle with side:▸ The angle given is between the rope and the ground, not between the rope and the pole.Not using a calculator for non-standard angles:▸ Although 30°, 45°, and 60° are standard, make sure you know their sine, cosine, and tangent values.Not visualizing the triangle:▸ Always sketch a triangle; it makes things easier to understand and solve.
📝 Related Questions:-
- 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 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.
- 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 Q6 - A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
- 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 Q1 Class 10
Class 10 Ex 9.1 Q1
Class 10 Chap 9 Ex 9.1 Q1
Class 10 Some Applications Of Trigonometry
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