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

On a plane area, there are two vertical towers separated by 100 feet apart. The shorter tower is 40 feet tall. A pole of length 6 feet stands on the line joining the base of two towers so that the tip of the towers and tip of the pole are also on the same line. If the distance of the pole from the shorter tower is 75 feet, then what is the height of the taller tower (approximately)?

  1. 85 feet

  2. 110 feet

  3. 125 feet

  4. 140 feet
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

The height of building A is 20 feet and the distance between the foot of building A and a car is 16 feet. The height of building B is 25 feet and the distance between the foot of the building and a bus is 'd'. If the distances are proportional to the heights of the buildings, then what would be the value of 'd', in feet?

  1. 5

  2. 10

  3. 15

  4. 20

  5. 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since the distances are proportional to the heights, we set up the ratio 20/16 = 25/d. Solving for d gives 20d = 16 * 25, which is 20d = 400, so d = 20.

Multiple choice

A 30-metre ladder is placed against a wall such that it just reaches the top of the wall. If the horizontal distance between the wall and the base of the ladder is 1 3 rd of the length of ladder, then the height of wall is:

  1. 25 metres

  2. 20 2 metres

  3. 20 3 metres

  4. 20 metres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The horizontal distance is 30/3 = 10 metres. By the Pythagorean theorem, the wall height is sqrt(30^2 - 10^2) = sqrt(800) = 20sqrt(2) metres, so option B is correct.

Multiple choice

In a city, there is a tall tower located at a point. Three observation points, X, Y and Z, are positioned at distances of 5 metres, 10 metres, and 20 metres, respectively, from the base of the tower. The angles of elevation of the top of the tower from X and Z are complementary. What is the height of the tower in metres?

  1. 5

  2. 10

  3. 20

  4. 30

  5. 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let height be h. Angles of elevation from X (5m) and Z (20m) are complementary (a and 90-a). tan(a) = h/5, tan(90-a) = h/20. Since tan(90-a) = cot(a) = 1/tan(a), we have h/20 = 1/(h/5) = 5/h. h^2 = 100, so h = 10.

Multiple choice

A driver is travelling along a straight highway with two prominent landmarks, Landmark X and Landmark Y. While driving, the driver notices something fascinating. After covering a distance of 300 metres from Landmark X, he observes that the angle of elevation to the top of Landmark X is 45 degrees, and the angle of elevation to the top of Landmark Y is 30 degrees. If Landmark Y has a height of 100 metres, determine the horizontal distance (in metres) between the tops of both Landmarks X and Y.

  1. 200 m

  2. 300 m

  3. 413.73 m

  4. 513.73 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

The horizontal distance between two towers is 75 mand the angular depression of the top of the first toweras seen from the top of the second which is 160 m highis 45°. Find the height of the first tower

  1. 75M

  2. 85M

  3. 89M

  4. 65M

  5. 82M
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the towers be T1 and T2. T2 height = 160m. Horizontal distance = 75m. Angle of depression = 45 degrees. The difference in height between the two towers is 75 * tan(45) = 75m. Height of T1 = 160 - 75 = 85m.