All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
2651
A tower is 50√3 m high. The angle of elevation of its top from a point 50 m away from its foot is:
Answer:
60°
Step 1: tan(θ) = Height / Distance = 50√3 / 50. Step 2: tan(θ) = √3. Step 3: θ = 60°.
2652
Find the distance of a point from the base of a tower 100 m high if the angle of elevation of the top is 60°.
Answer:
100/√3 m
Step 1: tan(60°) = Height / Distance. Step 2: √3 = 100 / d. Step 3: d = 100 / √3 m.
2653
The angle of elevation of the top of a tower from a point 20 m away from its base is 45°. What is the height of the tower?
Answer:
20 m
Step 1: tan(45°) = h / 20. Step 2: 1 = h / 20. Step 3: h = 20 m.
2654
From a point 50 m from the base of a building, the angle of elevation to the top is 60°. Find the height of the building.
Answer:
50√3 m
Step 1: tan(60°) = Height / Base. Step 2: √3 = h / 50. Step 3: h = 50√3 m.
2655
The angle of elevation of the top of a tower from a point on the ground 30 m away from the foot of the tower is 30°. Find the height of the tower.
Answer:
10√3 m
Step 1: tan(30°) = Height / Base. Step 2: 1/√3 = h / 30. Step 3: h = 30 / √3 = 10√3 m.
2656
A string of length 80 m is attached to a kite. If the height of the kite is 40 m, find the angle of elevation.
Answer:
30°
Step 1: sin(θ) = Height / Hypotenuse. Step 2: sin(θ) = 40 / 80 = 1/2. Step 3: Therefore, θ = 30°.
2657
If a 100 m string of a kite makes an angle of 60° with the ground, find the height of the kite.
Answer:
50√3 m
Step 1: sin(60°) = h / 100. Step 2: √3/2 = h / 100. Step 3: h = 100 * (√3/2) = 50√3 m.
2658
The string of a kite is 120 m long and makes an angle of 45° with the horizontal. Find the height of the kite.
Answer:
60√2 m
Step 1: sin(45°) = Height / Hypotenuse = h / 120. Step 2: 1/√2 = h / 120. Step 3: h = 120 / √2 = 60√2 m.
2659
A kite is flying at a height of 75 m. If the string makes an angle of 60° with the ground, what is the length of the string?
Answer:
50√3 m
Step 1: sin(60°) = Height / L. Step 2: √3/2 = 75 / L. Step 3: L = 150 / √3 = 50√3 m.
2660
A kite is flying at a height of 50 m above the ground. The string is inclined at 30° to the ground. Find the length of the string assuming there is no slack.
Answer:
100 m
Step 1: The height is the perpendicular (50 m) and the string is the hypotenuse (L). Step 2: sin(30°) = Height / L. Step 3: 1/2 = 50 / L, so L = 100 m.