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ECAT Mathematics Application of Trigonometry Online Test

Mustansar KhanLast Updated: April 18, 2025

Mathematics Application of Trigonometry MCQS Online Test

ECAT Math Application of Trigonometry Chapter Online Test

Total Questions:	45
Time Allowed:	20 Minutes
Total Marks:	45
How to Attempt Test:	Please choose the right Option in MCQ-type question.
Test Helpful For:	ECAT Entry Test Math Online Test Interview Questions about Math All Universities Entrance Test Recruitments Tests

ECAT Math Application of Trigonometry Test

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1. The angles of elevation of the top of a tower at the top and the foot of a pole of height 10 m are 30° and 60° respectively. The height of the tower is

15 m

20 m

10 m

None of these

2. 1/ab + 1/bc + 1/ca =

1/2rR

r/2R

R/2r

2rR

3. Circum radius of a circle is denoted by

r₂

4. The area of a triangle with a = 300, b = 120, ϒ = 150° is

5000 square units

9000 square units

7000 square units

6000 square units

5. Hero’s formula is used to calculate

Area of ∆

Angles of ∆

Sides of ∆

None of these

6. a/sina = b/sinβ – c/sinϒ is law of

Cotangent

Cosine

Tangent

Sine

7. A man of height 6 ft observes the top of a tower and the foot of the tower at angles of 45° and 30° of elevation and depression respectively. The height of the towers is

(1 + √3)m

3(1 + √3)m

None of these

6(1 + √3)m

8. R =

a/2sinβ

c/2sinϒ

a/2sina

a/2sinϒ

10.

11. 4 R sin a/2 sin β/2 sin ϒ/2 =

r₂

r₃

r₁

12. An airplane flying at a height of 300 meters above the ground passes vertically above another place at an instant when the angle of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Then the height of the lower plane from the ground is (in meters).

150(√3+1)

100/√3

100√3

13. If a = 13, b = 14, c = 15, then r₂ =

10.5

14. If ∆ is the area of a triangle ABC, then ∆ =

a²sina/2sinβ sinϒ

b²sina/2sinβ sinϒ

a²sinβ sinϒ/2 sin a

c²sina/2sinβ sinϒ

15. cot a/2 =

16. The point of intersection of the internal bisector of one angle and external bisectors of the other two angles of a triangle is known as

Circum – Center

In – center

None of these

Ex – center

17. r₃ =

s tan a/2

s tan a

s tan ϒ/2

s tan β/2

18. 4R cos ½ a sin ½ β cos ½ ϒ =

r₂

r₁

r₃

19.

20. If a flagstaff 6 meters high placed on the top of a tower throws a shadow of 2√3 meters along the ground then the angle (in degrees) that the sun makes with the ground is

60°

30°

45°

None of these

21. AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A. the portion CB subtends and angle β at P. If AP:AB = 2:1 then β =

tan⁻¹ 2/9

tan⁻¹ 5/9

tan⁻¹ 4/9

tan⁻¹ 1/9

22. If you are looking someone on the ground from the op a hill, the angle formed is the

Right angle

Angle of depression

Constant angle

Angle of elevation

23. At the top of a cliff 80 m high, the angle of depression of a boat is 12°. The distance of the boat from the cliff is

100 m

477 m