Some Applications of Trigonometry — Class 10 solved problems

32 problems from this chapter, each solved step by step.

A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30 degrees with it. The distance betwee
The height of the tree is 8√3 meters.
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60 degrees and the angle of depression of its foot is 45 degrees. Det
The height of the tower is 7(1 + √3) m.
The angle of elevation of the top of a building from a point on the ground is 30 degrees. On walking 20 m towards the building the angle becomes 60 degrees. Fin
The height of the building is 10√3 m.
A contractor plans to install a slide for children under 5. The top of the slide is at a height of 1.5 m, and it is inclined at an angle of 30° to the ground. W
The length of the slide should be 3 m.
A 1.5m tall boy is standing at some distance from a 32m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60°
The distance the boy walked towards the building is (61√3)/(3) m.
The angle of elevation of a cloud from a point h meters above a lake is α and the angle of depression of its reflection in the lake is β. Prove that the height
The height of the cloud is (h(tan β + tan α))/(tan β - tan α)
A vertical pole 12 m high casts a shadow 5√3 m long. Find the angle of elevation of the Sun.
The angle of elevation of the Sun is tan^(-1)((4√3)/(5)).
Heights and Distances From a point on the ground, the angle of elevation of the top of a tower is 45°. If the point is 30 m from the base of the tower, find the
The height of the tower is 30 m.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his
The distance the boy walked towards the building is 19√3 m (approximately 32.91 m).
A vertical tower stands on a horizontal plane. From a point on the ground 22 meters away from the base of the tower, the angle of elevation to the top of the to
The height of the tower is (22√3)/(3) meters.
STEP-BY-STEP DERIVATION 1 Identify the given information and unknown. Distance from tower base = 18 m Angle of elevation = 30^° Height of tower = h =? 2 Choose
The height of the tower is 6√3 m.
A vertical tower stands on a horizontal plane. From a point on the ground 18 meters away from the base of the tower, the angle of elevation to the top of the to
The height of the tower is 6√3 meters.
A vertical tower stands on a horizontal plane. From a point on the ground 17 meters away from the base of the tower, the angle of elevation to the top of the to
The height of the tower is (17√3)/(3) meters.
Chalkboard Explanation Video Step-by-step Derivation 1 Identify the given information and unknown Distance from base = 15 m Angle of elevation = 60^° Height of
The height of the tower is 15√3 m.
A vertical pole 10 m long casts a shadow of length 5 m on the ground. At the same time, a tower casts a shadow of length 12.5 m on the ground. The height of the
The height of the tower is 25 m.
Due to short circuit, a fire has broken out in New Home Complex. Two buildings, namely X and Y have mainly been affected. The fire engine has arrived and it has
(i) Length of the ladder = 15 m (ii) Distance of building Y from point 'O' (OA) = 7.5 m (iii) (a) Horizontal distance between the two buildings = 7.5 + 7.5√2 ≈
As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30^° to 45^°. Dete
The distance travelled by the ship is 73.2 m.
If the length of the shadow on the ground of a pole is √3 times the height of the pole, then the angle of elevation of the Sun is:
The angle of elevation of the Sun is 30^°.
The height of a tower is 20 m. The length of its shadow made on the level ground, when the sun's elevation is 60^°, is:
The length of the shadow is (20√3)/(3) m.
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 25 m high building are 30^° and 60^°
The height of the transmission tower is 50 m.
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30^° and 45^°, respectively. If the bridge is
The width of the river is 3(√3 + 1) meters.
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tow
The height of the tower is 15√3 m.
एक समतल जमीन पर खड़ी मीनार की छाया उस स्थिति में 40 m अधिक लंबी हो जाती है जबकि सूर्य का उन्नतांश (altitude) 60^° से घटकर 30^° हो जाता है। मीनार की ऊँचाई ज्ञात
मीनार की ऊँचाई 20 m है।
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30^° than when it is 60^°. Find the height of the tower.
The height of the tower is 20√3 m.
A 1.5m tall boy is standing at some distance from a 30m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60°
The distance the boy walked towards the building is 19√3 m.
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching th
The time taken by the car to reach the foot of the tower from point C is 3 seconds.
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45^°. What is the height of the chimney?
The height of the chimney is 30 m.
As observed from the top of a 100m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the
The distance between the two ships is 100(√3 - 1) m.
A kite is flying at a height of 60m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the strin
The length of the string is 40√3 m.
From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30^°. A flag is hoisted at the top of the building and the angle of el
The distance of the building from point P is 17.32 m and the length of the flagstaff is 7.32 m.
As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30^° to 45^°. Dete
The distance travelled by the ship is 73.2 m.
The angle of elevation of the top of a tower from a point on the ground 30 m away from the foot of the tower is 30 degrees. Find the height of the tower.
The height of the tower is 10√3 meters.

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