Question

After traveling 400m from a runway, a plane is 300m above the ground. Calculate its angle of

elevation.

Answer 1

Answer: It’s angle of elevation is 48.6 degrees (approximately)

Step-by-step explanation: Please refer to the picture attached for details.

If the plane travels for 400 meters from the runway and is currently at a height of 300 meters from the ground, then the plane is at point A. The distance travelled so far is line CA, while the height from the ground is line AB. The angle of elevation formed is at angle C where the plane started it’s journey.

To calculate angle we would use the trigonometric ratio since we have derived a right angled triangle with C as the reference angle and line AB as the opposite (facing the reference angle) and also line AC as the hypotenuse (longest side/side facing the 90 degree angle).

SinC = opposite/hypotenuse

SinC = 300/400

SinC = 3/4

SinC = 0.7500

From your calculator or a table of values,

C = 48.5903

Approximately angle C = 48.6 degrees

Answer 2

36.9°

Explanation:

With the details given to us in the question, we can easily understand that the plane formed a right angled triangle in terms of its shape,where the opposite/height of the triangle is 300m(since it says that the plane is 300m above the ground)

And the adjacent/base of the triangle is 400m (since the plane traveled a distance of 400m).

To find the angle of elevation,we are going to use SOH CAH TOA

Tangent x = opp/adj

Tan x = 300/400

Tan x = 0.75

X = tan inverse of 0.75

X = 36.9°