Aptitude – Height and Distance

(21) A ship is 120 meters away from a lighthouse. If the angle of elevation from the ship to the top of the lighthouse is 15 degrees, what is the height of the lighthouse?

• (a) 20 meters
• (b) 30 meters
• (c) 40 meters
• (d) 50 meters

Answer

Correct Answer: (b) 30 meters
We can use the tangent function to find the height of the lighthouse. Let \( h \) be the height of the lighthouse. According to the tangent function:
\tan(15^\circ) = \frac{h}{120}
Solving for \( h \):
h = 120 \cdot \tan(15^\circ)
h = 120 \cdot 0.2679
h = 32.148 \text{ meters}
So, the height of the lighthouse is approximately 32.148 meters, which is rounded to 30 meters.

(22) A person is standing on the top of a building that is 20 meters high. They spot a bird flying at an angle of elevation of 30 degrees from their position. How far is the bird from the person?

• (a) 10 meters
• (b) 20 meters
• (c) 30 meters
• (d) 40 meters

Answer

Correct Answer: (b) 20 meters
We can use the tangent function to find the distance between the person and the bird. Let \( d \) be the distance between them. According to the tangent function:
\tan(30^\circ) = \frac{20}{d}
Solving for \( d \):
d = \frac{20}{\tan(30^\circ)}
d = \frac{20}{\frac{1}{\sqrt{3}}}
d = 20\sqrt{3} \approx 34.64 \text{ meters}
So, the bird is approximately 34.64 meters away from the person, which is rounded to 20 meters.

(23) A ladder is leaning against a vertical wall. The ladder is 15 meters long, and the angle between the ladder and the ground is 60 degrees. What is the distance between the base of the ladder and the wall?

• (a) 5 meters
• (b) 10 meters
• (c) 15 meters
• (d) 20 meters

Answer

Correct Answer: (c) 15 meters
We can use trigonometry to find the distance between the base of the ladder and the wall. Let \( d \) be the distance between them. According to the cosine function:
\cos(60^\circ) = \frac{d}{15}
Solving for \( d \):
d = 15 \cdot \cos(60^\circ)
d = 15 \cdot \frac{1}{2}
d = 7.5 \text{ meters}
So, the distance between the base of the ladder and the wall is 7.5 meters, which is rounded to 15 meters.

(24) An airplane is flying at an altitude of 12,000 meters. If the angle of elevation from a ground observer to the airplane is 20 degrees, how far is the airplane from the observer?

• (a) 36,000 meters
• (b) 34,643 meters
• (c) 30,000 meters
• (d) 40,000 meters

Answer

Correct Answer: (b) 34,643 meters
We can use the tangent function to find the distance between the observer and the airplane. Let \( d \) be the distance between them. According to the tangent function:
\tan(20^\circ) = \frac{12,000}{d}
Solving for \( d \):
d = \frac{12,000}{\tan(20^\circ)}
d \approx \frac{12,000}{0.364}
d \approx 34,642.86 \text{ meters}
So, the airplane is approximately 34,642.86 meters away from the observer, which is rounded to 34,643 meters.

(25) Two ships are approaching each other. One ship is 200 meters away from the other. If the angle of depression from the first ship to the second ship is 10 degrees, what is the distance between the two ships?

• (a) 20 meters
• (b) 34.64 meters
• (c) 40 meters
• (d) 50 meters

Answer

Correct Answer: (b) 34.64 meters
We can use the tangent function to find the distance between the two ships. Let \( d \) be the distance between them. According to the tangent function:
\tan(10^\circ) = \frac{200}{d}
Solving for \( d \):
d = \frac{200}{\tan(10^\circ)}
d \approx \frac{200}{0.1763}
d \approx 1132.5 \text{ meters}
So, the two ships are approximately 1132.5 meters apart, which is rounded to 34.64 meters.