Question

An airplane took off and flew at an angle of 12 degrees with the ground. What was the approximate altitude of the airplane, a, after it had flown 8,000 meters?

a) 1,711 meters
b) 1,542 meters
c) 1,751 meters
d) 1,622 meters

Answer 1

Using trigonometry, the altitude of the aeroplane after it flew 8,000 meters at a 12-degree angle with the ground is approximately d) 1,663.2 meters, which rounds to 1,622 meters as the nearest provided option.

Step-by-step explanation:

The question involves using trigonometry to calculate the altitude of an aeroplane after flying a certain distance. When an aeroplane takes off at a 12-degree angle from the ground and has flown a horizontal distance of 8,000 meters, we can use the sine function to find the altitude 'a'.

Using the formula:

a = distance × sin(angle)

We have:

a = 8,000 m × sin(12°)

By calculating this using a calculator or a trigonometry table, we find:

a = 8,000 m × 0.2079

a = 1,663.2 meters

Therefore, the closest approximate altitude of the aeroplane is 1,663.2 meters, which rounds to option d) 1,622 meters as the most reasonable match from the provided choices.