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

From the top of a building 60m high, the angle of elevation and depression of the top and the foot of another building are α and β respectively. Find the height of the second building.

  1. 60(1+ tan α tanβ)

  2. 60(1+ cot α tanβ)

  3. 60(1+ tan α cotβ)

  4. 60(1- tan αcotβ)

  5. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the first building be AB (60m) and the second be CD. The distance between them is d. From the top of AB, the angle of depression to the foot of CD is beta, so tan(beta) = 60/d, d = 60 * cot(beta). The angle of elevation to the top of CD is alpha, so the height of the part of CD above the level of A is d * tan(alpha) = 60 * cot(beta) * tan(alpha). Total height = 60 + 60 * cot(beta) * tan(alpha) = 60(1 + tan(alpha) * cot(beta)).

Multiple choice

A tower, stationed at the center of a circular park, is casting a shadow. A person standing at the east side of the tower is making an angle of 45° with the top of the tower. Simultaneously, another person, stationed at the west side of the tower, is making an angle of 60° with the top of the tower. The height of the tower is 400 feet. What is the approximate shortest distance between these two persons? Assume both persons are of negligible dimensions.

  1. 425

  2. 452

  3. 631

  4. 842
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The tower height h = 400. For the person at 45 degrees, the distance from the tower base is d1 = h / tan(45) = 400. For the person at 60 degrees, the distance is d2 = h / tan(60) = 400 / sqrt(3) approx 230.94. The total distance is d1 + d2 = 400 + 230.94 = 630.94, which rounds to 631.

Multiple choice

The horizontal distance between 2 towers is 70 m.The angle of depression of the top of the first tower when seen from the top of the second tower is 30º. If the height of the second tower is 120 m, find the height of the first tower.

  1. 138.8 m

  2. 84.6 m

  3. 101.6 m

  4. 79.6 m

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let h be the height of the first tower. The difference in height is 120 - h. tan(30) = (120 - h) / 70. 1/sqrt(3) = (120 - h) / 70. 120 - h = 70 / 1.732 = 40.41. h = 120 - 40.41 = 79.59 m.

Multiple choice

In a room, a man is standing on the ladder, which rests against a wall with its lower end at a distance X from the wall and its upper end at a height 2X above the floor. Due to the weight of the man, the lower end slides through a distance Y perpendicular to the edge between the floor and the wall, by how much does the upper end slide?

  1. X √5 - √5X2 - (X - Y)2

  2. X √5 + √5X2 - (X+ Y)2

  3. 2X - √ {5X2 - (X + Y)2

  4. 2X + √5X2 - (X - Y)2

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the Pythagorean theorem, the ladder length L satisfies L^2 = X^2 + (2X)^2 = 5X^2. After sliding, the new height h satisfies (X+Y)^2 + h^2 = 5X^2, so h = sqrt(5X^2 - (X+Y)^2). The vertical slide is 2X - h.

Multiple choice

From two points A and B on the same side of a building, that are in a straight line with it, the angles of elevation of the top of the building are 30° and 60° respectively. If the distance between the two points is 50 m, what is height of the building?

  1. 25.5 m

  2. 40.3 m

  3. 43.3 m

  4. 30.3 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let height be h. Distance from building is h/tan(60) and h/tan(30). The difference is h/tan(30) - h/tan(60) = 50. So h * (sqrt(3) - 1/sqrt(3)) = 50, which simplifies to h * (2/sqrt(3)) = 50, so h = 25 * sqrt(3) approx 43.3 m.

Multiple choice

Two poles of height 15 metres and 30 metres stand upright on a playground. If the feet of the poles are 36 metres apart, the distance between their tops is

  1. 35 metres

  2. 37 metres

  3. 39 metres

  4. 41 metres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The distance between the tops of two vertical poles can be found using the Pythagorean theorem. The horizontal distance is 36m and the vertical difference in height is 30 - 15 = 15m. The distance is sqrt(36^2 + 15^2) = sqrt(1296 + 225) = sqrt(1521) = 39m.

Multiple choice

Directions : Answer the question independently. Two poles, one 78 m in height above the ground and the other 91 m in height above the ground, are at some distance from each other. Two strings are tied, one from the top of one pole to the bottom of the other and the other from the top of the second pole to the bottom of the first. Find the height (in m) above the ground at which the strings intersect. Assume strings are taut.

  1. 42m

  2. 50m

  3. 39 m

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The height of intersection h for two poles of height h1 and h2 is given by the formula h = (h1 * h2) / (h1 + h2). Here, h = (78 * 91) / (78 + 91) = 7098 / 169 = 42 m.

Multiple choice

There are two upright poles of height 20√3 m and 30√3 m respectively separated by a distance of 40 m. A man is standing between the two poles. What is the probability that the angle elevation of the top of the poles as seen by the man is at least 60°?

  1. 1/8

  2. 1/5

  3. 1/3

  4. 1/4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the man be at distance x from the first pole (20sqrt(3)m). The angle of elevation is >= 60 degrees if tan(theta) = h/d >= sqrt(3). For the first pole, x <= 20sqrt(3)/sqrt(3) = 20. For the second pole, (40-x) <= 30sqrt(3)/sqrt(3) = 30. Thus, x <= 20 and x >= 10. The favorable range for x is [10, 20], which has length 10. The total distance is 40, so probability is 10/40 = 1/4.

Multiple choice

A child is initially standing at a point on the ground, observing the top of a building, which has a height of 50 metres. The angle of elevation from the child's position to the top of the building is 30°. After walking a certain distance, denoted as d, towards the building, the angle of elevation increases by 15° from the original angle. Determine the distance (d) in cm the child walked towards the building.

  1. 360

  2. 366

  3. 3,660

  4. 36,600
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial distance x = 50 / tan(30) = 50 * sqrt(3). Final distance y = 50 / tan(45) = 50. Distance walked d = x - y = 50(sqrt(3) - 1) = 50(1.732 - 1) = 50 * 0.732 = 36.6 meters. Convert to cm: 36.6 * 100 = 3660 cm.

Multiple choice

Directions: The question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the question. Using the data, mark your answer as What is the distance between the two ships? I. Seen from the top of a mountain, their angles of depression are 60o and 30o. II. Height of the mountain is 60 metres.

  1. if statement I alone is sufficient to answer the question

  2. if statement II alone is sufficient to answer the question

  3. if both statements I and II are sufficient to answer the question, but neither statement alone is sufficient

  4. if both statements I and II together are not sufficient to answer the question and additional data is required
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: Each question is followed by two statements. Mark [1], if the question can be answered by using only one of the statements alone but not by using the other statement alone Mark [2], if the question can be answered by using either of the statements alone. Mark [3], if the question can be answered by using both the statements together but not by using either of the statements alone. Mark [4], if the question cannot be answered. What is the height of a tower installed on the top of a hill? I: Angle of elevation made by the bottom of the tower is 45 degrees and the top of the tower is 60 degrees from a point at a distance 'a' from the foot of the hill in the eastern direction. II: Angle of elevation made by the bottom of the tower is 30 degrees from a point at a distance 'a + 10' from the foot of the hill in the eastern direction.

  1. 1

  2. 2

  3. 3

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

Statement I gives two angles from one point, allowing calculation of the tower height using trigonometry. Statement II gives one angle from a different point. Both are needed to define the geometry fully relative to the hill height and distance 'a'.