Abird sitting on top of a stop sign notices a piece of food on the ground, 11 ft from the base of the stop sign. if the bird has to look down at a 39° angle of depression in order to see the piece of food, what is the approximate distance from the bird to the food?

14.15ft

Step-by-step explanation:

Attached is a visual representation of our scenario.

The green line represents the line of sight of the bird, and the green angle represents the angle of depression. It goes downwards because it says "depression."

As you can observe, the scenario creates a right triangle, where the alternate interior of the angle is found in the triangle.

Using Trigonometric Functions, or SOHCAHTOA, we can solve for the distance between the bird and the food, which in this case is the hypotenuse(H) of the triangle. Looking at the diagram again, we can see that 11ft was also given, which can be represented as the adjacent (A) side of the triangle. It is adjacent because it is right next to the angle given.

Because we have an angle and the adjacent side, we will use CAH.

Given:

A= 11ft

H = x

θ = 39°

Solution:

CAH

The bird is 14.15 ft away from the food.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc