An airplane flies at an altitude of 3.2 km. The angle of depression from the plane to the base of a building is 52 degrees . How far horizontally must the plane fly to be directly above the building?
Question
An airplane flies at an altitude of 3.2 km. The angle of depression from the plane to the base of a building is 52 degrees . How far horizontally must the plane fly to be directly above the building?
Solution
To solve this problem, we can use the tangent of the angle of depression, which is the ratio of the opposite side (the altitude of the plane) to the adjacent side (the horizontal distance we want to find).
Here are the steps:
-
Convert the altitude of the plane from kilometers to meters because the standard unit of measurement in trigonometry problems is meters. So, 3.2 km = 3200 meters.
-
The angle of depression is the same as the angle of elevation from the building to the plane, which is 52 degrees.
-
Set up the equation using the tangent of the angle of depression (which is the same as the angle of elevation from the ground): tan(52) = 3200 / x, where x is the horizontal distance from the plane to the building.
-
Solve the equation for x: x = 3200 / tan(52).
-
Use a calculator to find the value of x: x ≈ 2400 meters.
So, the plane must fly approximately 2400 meters horizontally to be directly above the building.
Similar Questions
An airplane flies at an altitude of 3.2 km. The angle of depression from the plane to the base of a building is 52 degrees . What trigonometric function (s) will be able to determine the horizontal distance must the plane fly to be directly above the building? Check all that applies.
The angle of elevation from the top of a small building to the top of a nearby taller building is 46°40′, while the angle of depression to the bottom is 14°10′. If the shorter building is 28.0 m high, which of the following equations solves for the distance between the buildings? Let x be the distance between the buildings.
From the top of a 35-meter building you can see an angle of depression of 18° to point A. What is the distance from the base of the building to point A?
The angle of elevation of the top of a building 30 m high from a point in the same plane is 60º, then the distance of the point from the foot of the building is
On the top of the tower 100 meters high, Brianne saw and fell in love with Jo who is sitting under the tree. How far is Jo from the tower if the angle of depression formed by Brianne’s line of sight with the horizontal is 30°?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.