SSC CHSL Topic Wise Study Material - Quantitative Aptitude - Height and Distance

SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Height and Distance

Contents

SSC CHSL Study Material SSC CHSL Previous Papers SSC CHSL Practice Workbook

Height and distance is an essential component of Trigonometry.
In this chapter trigonometric properties are used for finding height and distances of various objects without actually measuring it. Sometimes we are required to find the height of a tower, tree, building and distance of a ship from light house, width of a river.

Concept of Pythagoras Theorem
In a right angled triangle, the square of its hypotenuse is equal to the sum of the squares of its legs (i.e., perpendicular and base).

In other words, (Hypotenuse)² = (Perpendicular)² + (Base)²
=> (BC)² = (AB)² + (AC)² => h²=p² + b²
Pythagoras theorem is used for solving most of the problems of height and distance.

Angle of Elevation The angle of elevation of the point viewed is the angle formed by the line of horizontal, when the point being is above the horizontal level.

Example A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30°. The man walks some distance towards the tower and then his angle of elevation of the top of the tower is 60°. If the height of the tower is 30 m, then the distance he moves is
(a) 20 m
(b) 20√3 m
(c) 22 m
(d) 22√3 m

Angle of Depression When the line of sight is below the horizontal level, the angle so formed by the line of sight with the horizontal is called the angle of depression.

Example From a point A 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 at a height of 9 m from the banks, find the width of the river.
(a) 24.588 m
(b) 23.458 m
(c) 25.458 m
(d) 28.885 m

Reference Corner

1. TF is a tower with F on the ground. The angle of elevation of T from A is x° such that tan x° = 2/5 and AF= 200 m. The angle of elevation of T from a nearer point B is y° with BF = 80 m. The value of y° is SSC (10 + 2) 2015
(a) 75°
(b) 45°
(c) 60°
(d) 30°

2.A tree of height h m is broken by a storm in such a way that its top touches the ground at a distance of x m from its root. Find the height at which the tree is broken. (Here, h > x) SSC (10+2) 2014
(a)h²+x²/4h m
(b)h²-x²/4h m
(c)h²+x²/2h m
(d)h²-x²/2h m

3. The angle of elevation of the top of a tower from a point on the ground is 30° and moving 70 m towards the tower it becomes 60°. The height of the tower is SSC (10+2) 2014
(a) 10√3 m
(b) 35√3 m
(c) 10 m
(d) 10/√3 m

4. From two points on the ground and lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distances of the two points from the foot of the pillar are 9 m and 16 m and the two points lie on the same side of the pillar, then the height of the pillar is SSC (10 + 2) 2013
(a) 7 m
(b) 12 m
(c) 5 m
(d) 10 m

Practice Exercise

1. The angle of elevation of the top of a tower at a point D on the ground is 30°. On walking 20 m towards the tower the angle of elevation becomes 60°. The height of the tower is equal to
(a)10/√3 m
(b)20√3 m
(c)20/√3 m
(d)10√3 m

2. A radio transmitter antenna pf height 100 m stands at the top of a tall building. At a point on the ground, the angle of elevation of bottom of the antenna is 45° and that of top of antenna is 60°. What is the height of the building?
(a) 100 m
(b) 50 m
(c) 50 (√3 + 1) m
(d)50 (√3 – 1)m

3. The angle of elevation of a jet fighter from a point P on the ground is 60°. After 5 s of flight, the angle of elevation changes to 45°. If the jet is flying at a height of 3000 m, then the speed of the jet (in m/s) is
(a) 1000 (3 – √3)
(b) 200 (3 – √3)
(c)1000√3
(d) 600

4. From the mast head of ship, the angle of depression of a boat is 60°. If the mast head is 150 m, then the distance of the boat from the ship is
(a) 86.6 m
(b) 68.6 m
(c) 66.8 m
(d) None of these

5. A telegraph post gets broken at a point against a storm and its top touches the ground at a distance 20 m from the base of the post making an angle 30° with the ground. What is the height of the post?
(a) 40/√3 m
(b) 20√3 m
(c) 40√3 m
(d) 30 m

6. A portion of a 30 m long tree is broken by tornado and the top struck up the ground making an angle 30° with ground level. The height of the point where the tree is broken, is equal to
(a)30/√3m
(b)10m
(c) 30√3 m
(d) 60 m

7. The angle of elevation of the top of a tower from the bottom of a building is twice that from its top. What is the height of the building if the height of the tower is 75 m and the angle of elevation of the top of the tower from the bottom of the buildings is 60°?
(a) 25 m
(b) 37.5 m
(c) 50 m
(d) 60 m

8. The shadow of a tower is 15 m when the elevation is 30°. What is the length of the & when the sun’s elevation is 60°?
(a) 3 m
(b) 4 m
(c) 5 m
(d) 6 m

9. Two posts are 25 m and 15 m high and the joining their tips makes an angle of 45° horizontal. The distance between these posts is
(a) 5 m
(b) 10/√2 m
(c) 10 m
(d)10√2 m

10. The poles of heights 6 m and 11 m stand vertically upright on a plane ground. If the distance between their feet is 12 m. What is the distance between their tops?
(a) 11 m
(b) 12 m
(c) 13 m
(d) 14 m

11. The height of a tower is h and the angle of elevation of the top of the tower is α. On moving a distance h/2 towards the tower, the angle of elevation becomes β. What is the value of (cot α – cot β)?
(a)1/2
(b)2/3
(c)1
(d)2

12. A vertical post 15 ft high is broken at a certain height and its upper part, not completely separated, meets the ground at an angle of 30°. Find the height at which the post is broken. SSC (10 + 2) 2012
(a) 10 ft
(b) 5 ft
(c) 15√3 (2 – √3) ft
(d)5√3 ft

13.The angles of elevation of the top of a building from the top and bottom of a tree are x and y, respectively. If the height of the tree is h m, then in metre, the height of the building is SSC (10+2) 2011