Quantitative Aptitude

Trigonometry

435 Questions
All Height and Distance 268 Triangle Properties and Rules 50 Standard Angle Evaluation 33 Complementary and Odd-Even Angles 30 Value of one ratio from another 26 Trigonometric Identities 14 Maxima and Minima 6 General and Principal Solutions 5 Quadratic Substitution 3

Trigonometry Questions

Multiple choice

A man is standing on the top of a raised platform such that his eyes are 3 m high from the horizontal ground level and at a horizontal distance of 30 m from a tree. The angle of elevation of the top of the tree from his eyes is 30°. Estimate the height of the tree.

  1. 17.16 m

  2. 24.6 m

  3. 20.32 m

  4. 21.94 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The height of the tree above the eye level is 30 * tan(30) = 30 * (1/sqrt(3)) = 10 * sqrt(3) approx 17.32 m. Total height = 17.32 + 3 = 20.32 m.

Multiple choice

Two buildings AB and CD are such that height AB is greater than height CD. The perpendicular distance between two buildings is 100 m. The angle of elevation of top of building AB from the top of building CD is 60o. The distance between tops of buildings will be

  1. 100 m

  2. 200 m

  3. 300 m

  4. 400 m

  5. 500 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the height difference be h. tan(60) = h / 100, so h = 100 * sqrt(3). The distance between the tops is the hypotenuse of a triangle with base 100 and height h. Distance = sqrt(100^2 + (100*sqrt(3))^2) = sqrt(10000 + 30000) = sqrt(40000) = 200.

Multiple choice

The upper part of a tree, broken over by the wind, makes an angle of 60° with the ground. The distance between the root and the point where the top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree?

  1. 84.14

  2. 93.3

  3. 98.25

  4. 120.24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the broken part be h and the standing part be x. The distance from the root is 25. tan(60) = h/25 is incorrect; rather cos(60) = 25/hypotenuse, so hypotenuse = 50. tan(60) = height_standing / 25, so height_standing = 25 * sqrt(3) = 43.3. Total height = 50 + 43.3 = 93.3.

Multiple choice

Two poles P and Q of equal height are standing in a plane. The distance between the poles P and Q is 100 m. The respective angles of elevation of the top of the poles P and Q from a point on the ground, lying between both poles, are 60o and 30o respectively. If the height of the poles is h and the distance of the point from the pole P is x, then find the values of h and x. (Take √3 = 1.732)

  1. h = 40 m and, x = 25 m

  2. h = 43 m and, x = 20 m

  3. h = 43.3 m and, x = 25 m

  4. h = 40.3 m and, x = 35 m

  5. h = 40.3 m and, x = 2.5 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let height be h. tan(60) = h/x => h = x*sqrt(3). tan(30) = h/(100-x) => h = (100-x)/sqrt(3). Equating: x*sqrt(3) = (100-x)/sqrt(3) => 3x = 100 - x => 4x = 100 => x = 25. h = 25 * 1.732 = 43.3 m.

Multiple choice

The horizontal distance between the two towers is 60 m. The angular elevation of the top of the taller tower as seen from the top of the shorter one is 30°. If the height of the taller tower is 150 m, then the approximate height of the shorter tower is

  1. 115 m

  2. 100 m

  3. 80 m

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let h be the height of the shorter tower. The difference in height is 150 - h. tan(30) = (150 - h) / 60. 1/sqrt(3) = (150 - h) / 60. 60 / 1.732 = 150 - h. 34.64 = 150 - h. h = 115.36.

Multiple choice

The height of two poles are 80 m. and 63.5 m. If the line joining their tops makes an angle of 45o with the horizontal, then the distance between the poles is -

  1. 16.5 m.

  2. 56.4 m.

  3. 12.33 m.

  4. 44 m.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The height difference between poles is 80 - 63.5 = 16.5 m. Since the line joining tops makes a 45° angle with horizontal, the horizontal distance equals the vertical difference. Using tan45° = 1 = opposite/adjacent, the distance = 16.5 m. This matches the claimed answer A.

Multiple choice

The angle of elevation of the top of a tower at a horizontal distance equal to the height of the tower from the base of the tower is -
  1. $30o$
  2. $45o$
  3. $60o$
  4. $75o$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let tower height = h. Observer is at horizontal distance h from base. This forms a right triangle with base = h and height = h. The angle of elevation satisfies tan(θ) = opposite/adjacent = h/h = 1. Therefore θ = 45°. Option A (30°) would require horizontal distance = h√3. Option C (60°) would require horizontal distance = h/√3.