An aeroplane leaves a runway and climbs at an angle of 15 degrees. After flying 800 meters, how high is it above the runway?

h/800 = sin 15°

To find the height of the airplane above the runway, we can use the concept of trigonometry.

First, let's draw a diagram to visualize the situation. The horizontal distance the airplane travels is 800 meters, and the angle of ascent is 15 degrees.

Now, we can use the trigonometric relationship of opposite and adjacent sides in a right triangle. In this case, the height of the airplane above the runway is the opposite side, and the horizontal distance is the adjacent side.

The trigonometric function that relates these sides is the tangent function (tan). We can use the formula:

tan(θ) = opposite / adjacent,

where θ represents the angle of ascent.

Rearranging the formula, we have:

opposite = tan(θ) * adjacent.

Plugging in the values from the problem:

opposite = tan(15 degrees) * 800 meters.

To evaluate this expression, we can use a calculator or look up the tangent of 15 degrees.

Using trigonometric tables or a calculator, the tangent of 15 degrees is approximately 0.268.

So, the height above the runway is:

opposite = 0.268 * 800 meters,

opposite ≈ 214.4 meters.

Therefore, the airplane is approximately 214.4 meters above the runway after flying 800 meters.