Nisha is looking out the window of her apartment building at a sculpture in a park across the street. the top of nisha's window is 90 feet from the ground. the angle of depression from the top of nisha's window to the bottom of the sculpture is 22°. how far away from the building is the sculpture? round your answer to the nearest hundredth.

222.76 feet

Step-by-step explanation:

This question can be solved using one of the three trigonometric ratios. The height mentioned is 90 feet and the angle of depression is 22 degrees. It can be seen that the required distance is given by x feet. This forms a right angled triangle, as it can be seen in the diagram. The perpendicular is given by 90 feet, the base is the unknown, and the angle of 22 degrees is given, as shown in the attached diagram. Therefore, the formula to be used is:

tan θ = Perpendicular/Base.

Plugging in the values give:

tan 22 degrees = 90/x.

x = 90/tan 22.

x = 222.76 feet (to the nearest hundredth).

Therefore, the building is 222.76 feet away from the sculpture!!!

The distance from Nisha's apartment building to a sculpture in a park across the street is 222.76 ft. You can solve for how far away the building is from the sculpture using trigonometric functions. Trigonometric functions are the basis of trigonometry. This branch of mathematics studies the sides and angle relationships of triangles. The main functions in trigonometry are Sine, Cosine, and Tangent.

a. Draw the Scenario:

Nisha's apartment building forms a right triangle with the sculpture in the park. Draw the scenario by using the steps below to guide you.

You can check your picture by clicking on the attachment.

b. Choose the function

Trigonometry has three main functions: sine, cosine, and tangent. Each function describes a ratio between the opposite, adjacent and hypotenuse sides of a triangle using a reference angle.

Here, use the angle of depression as the reference angle. The height is opposite the angle of depression. The base, how far away from the sculpture, is the adjacent side of the angle. Use the tangent function.

c. Calculate and round your answer.

Use the definition of tangent and a calculator to find your answer.

Grade: High School

Subject: Trigonometry

Chapter: Trigonometric Functions

Keywords: angle of depression, angle of elevation, tangent, sine, cosine, trigonometry, trigonometric, right triangle

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4