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

What was Brahmagupta's formula for the cosine of an angle?

  1. $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
  2. $\cos \theta = \frac{\text{opposite}}{\text{hypotenuse}}$
  3. $\cos \theta = \frac{\text{opposite}}{\text{adjacent}}$
  4. $\cos \theta = \frac{\text{hypotenuse}}{\text{adjacent}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for the cosine of an angle is $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$.

Multiple choice

A surveyor measures the angle of elevation to the top of a building to be 30 degrees. If the distance from the surveyor to the base of the building is 100 meters, what is the height of the building?

  1. 50 meters

  2. 75 meters

  3. 100 meters

  4. 125 meters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using trigonometry, the height of the building can be calculated using the tangent function.

Multiple choice

A kite is flying at a height of 100 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, what is the horizontal distance between the point and the base of the kite?

  1. 50 meters

  2. 75 meters

  3. 100 meters

  4. 125 meters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Trigonometry can be used to calculate the horizontal distance using the tangent function.

Multiple choice

What is the value of the cosecant of 45 degrees?

  1. 1.414

  2. 2

  3. 2.732

  4. 3.464
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cosecant of 45 degrees is 1.414.

Multiple choice

What is the formula for calculating the cosine of an angle in a right triangle?

  1. $$cos \theta = \frac{opposite}{hypotenuse}$$
  2. $$cos \theta = \frac{adjacent}{hypotenuse}$$
  3. $$cos \theta = \frac{opposite}{adjacent}$$
  4. $$cos \theta = \frac{hypotenuse}{opposite}$$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The formula for calculating the cosine of an angle in a right triangle is $$cos \theta = \frac{adjacent}{hypotenuse}$$

Multiple choice

What is the formula for calculating the cosecant of an angle in a right triangle?

  1. $$cosec \theta = \frac{hypotenuse}{opposite}$$
  2. $$cosec \theta = \frac{hypotenuse}{adjacent}$$
  3. $$cosec \theta = \frac{opposite}{hypotenuse}$$
  4. $$cosec \theta = \frac{adjacent}{opposite}$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the cosecant of an angle in a right triangle is $$cosec \theta = \frac{hypotenuse}{opposite}$$

Multiple choice

What is the value of the sine of an angle of 30 degrees?

  1. 0.5

  2. 0.6

  3. 0.7

  4. 0.8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sine of an angle of 30 degrees is 0.5.

Multiple choice

What is the value of the expression cot(45°)?

  1. 1

  2. √2

  3. √3

  4. 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The value of the expression cot(45°) is equal to 1.

Multiple choice

What is the value of the cosecant of 30 degrees according to Aryabhata?

  1. 0.5

  2. 0.866

  3. 1

  4. 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Aryabhata calculated the cosecant of 30 degrees to be 2, which is an accurate approximation.

Multiple choice

A ladder is leaning against the wall. The top of the ladder touches the wall at a height of 15 m. If the length of the ladder is 1 m more than twice its distance from the wall, find the distance from the wall to the bottom of ladder.

  1. 14 m

  2. 12 m

  3. 9 m

  4. 8 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance from wall be x. Ladder length L = 2x + 1. Height = 15. By Pythagoras: x^2 + 15^2 = (2x + 1)^2. x^2 + 225 = 4x^2 + 4x + 1. 3x^2 + 4x - 224 = 0. Using quadratic formula: x = (-4 + sqrt(16 - 4*3*(-224))) / 6 = (-4 + sqrt(16 + 2688)) / 6 = (-4 + 52) / 6 = 48 / 6 = 8.

Multiple choice

The angle of elevation of the top of a tower from a point on the ground at some distance from its base is 60°. The angle of elevation of the top of the tower from a point 20 m above the same point on the ground is 30°. What is the height of the tower?

  1. 30 m

  2. 20 m

  3. 15 m

  4. 10 m

  5. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let h be height, d be distance. tan(60) = h/d => d = h/sqrt(3). tan(30) = (h-20)/d => d = (h-20) * sqrt(3). Equating: h/sqrt(3) = (h-20) * sqrt(3) => h = 3(h-20) => h = 3h - 60 => 2h = 60 => h = 30.