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
1891
From the top of a 50 m high tower, the angle of depression of a car on the ground is 30°. Find the distance of the car from the foot of the tower.
Answer:
50√3 m
Step 1: The angle of depression is equal to the angle of elevation from the car to the top of the tower, which is 30°. Step 2: Let the distance be x. tan(30°) = height / distance = 50 / x. Step 3: 1 / √3 = 50 / x, so x = 50√3 m.
1892
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?
Answer:
30 m
Step 1: The horizontal distance from the observer to the chimney is 28.5 m. The angle of elevation is 45°. Step 2: The height of the chimney above the observer's eye level is h'. tan(45°) = h' / 28.5, so h' = 28.5 m. Step 3: Total height of the chimney = h' + observer's height = 28.5 + 1.5 = 30 m.
1893
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming there is no slack.
Answer:
40√3 m
Step 1: Let the length of the string be L. The height is the opposite side (60 m). Step 2: sin(60°) = opposite / hypotenuse = 60 / L. Step 3: √3 / 2 = 60 / L. Therefore, L = 120 / √3 = 40√3 m.
1894
The angle of elevation of a ladder leaning against a wall is 45°, and the foot of the ladder is 10 m away from the wall. What is the height of the wall where the ladder touches?
Answer:
10 m
Step 1: Let the height of the wall be h. The distance from the foot is 10 m. Step 2: tan(45°) = height / base = h / 10. Step 3: Since tan(45°) = 1, h / 10 = 1, resulting in h = 10 m.
1895
A ladder leans against a wall making an angle of 60° with the ground. If the foot of the ladder is 5 m away from the wall, find the length of the ladder.
Answer:
10 m
Step 1: The ladder forms the hypotenuse of a right-angled triangle. Let its length be L. Step 2: The base is 5 m, and the angle with the ground is 60°. Use cos(60°) = base / hypotenuse. Step 3: cos(60°) = 1/2. So, 1/2 = 5 / L, which gives L = 10 m.
1896
From a point 20 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower.
Answer:
20 / √3 m
Step 1: Let the height of the tower be h. The distance from the foot is 20 m. Step 2: tan(30°) = h / 20. Step 3: Since tan(30°) = 1 / √3, we have 1 / √3 = h / 20. Thus, h = 20 / √3 m.
1897
If the height of a pole is √3 times the length of its shadow, what is the angle of elevation of the sun?
Answer:
60°
Step 1: Let the shadow length be x. Then the height of the pole is x√3. Step 2: tan(θ) = height / shadow = (x√3) / x = √3. Step 3: Since tan(60°) = √3, the angle of elevation is 60°.
1898
The length of the shadow of a vertical pole is √3 times its height. Find the angle of elevation of the sun.
Answer:
30°
Step 1: Let the height of the pole be h. The shadow is h√3. Step 2: The tangent of the angle of elevation θ is height / shadow = h / (h√3) = 1 / √3. Step 3: We know that tan(30°) = 1 / √3. Hence, the angle is 30°.
1899
If the height of a vertical pole is equal to the length of its shadow on the ground, what is the angle of elevation of the sun?
Answer:
45°
Step 1: Let the height of the pole be h and the length of the shadow be x. Given h = x. Step 2: Let the angle of elevation be θ. Then tan(θ) = h / x. Step 3: Since h = x, tan(θ) = 1. Therefore, θ = 45°.
1900
How many degrees does the minute hand move in the same time the hour hand moves by 15°?
Answer:
180°
The hour hand moves 0.5° per minute. To move 15°, it requires 15 / 0.5 = 30 minutes. In 30 minutes, the minute hand moves 30 × 6° = 180°.