Question

If the distance from the top of a building to the tip of its shadow is 150 feet and the sun makes a 75 degree angle with the wall as shown in the image below, what is the length of the shadow?
144.89 feet

965.9 feet

53.4 feet

72.44 feet

Answer 1

The length of the shadow is 144.89 feet. The distance from the top of a building You can solve for the length of the shadow formed by the sun across a building 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.  

Further Explanation

a. Draw the Scenario:

The building forms a right triangle with its shadow. Draw the scenario by using the steps below to guide you.

1. The top of a building to the tip of its shadow is 150 feet and is drawn as a the diagonal line called a hypotenuse.
2. The distance between the building and the tip of its shadow is the distance you need to find. This forms the base of the triangle and is labeled with the variable x.  
3. The reference angle is 75 degrees and is formed by the building and the sun. It should be labeled at the top of the building

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.  

• Sine is the ratio of sides opposite over hypotenuse to the angle.
• Cosine is the ratio of sides adjacent over hypotenuse to the angle.
• Tangent is the ratio of sides opposite over adjacent to the angle.

Here, the distance from the top of the building to the tip of its shadow is the hypotenuse. The the distance between the building and the tip of its shadow is opposite the reference angle. Use the sine function.

c. Calculate and round your answer.

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

$sin(\alpha) = \frac{opposite}{hypotenuse}\\\\sin (75) = \frac{x}{150} \\\\x = sin (75)*150 \\\\x = 144.89 ft$

Learn More

• Trig ratios and Functions: brainly.com/question/12390405

• Application of Trig Functions: brainly.com/question/10546617

• Angle of Elevation and Depression: brainly.com/question/9817377

Answer Details

Grade: High School

Subject: Trigonometry

Chapter: Trigonometric Functions

Keywords: reference angle, sine, trigonometry, trigonometric function, opposite, hypotenuse, right triangle

Read more on Brainly.com - brainly.com/question/10546617

Answer 2

By the process of elimination I believe that the angle the sun makes with the building is the vertex angle.  If that is our reference angle, we have the hypotenuse as 150 and we are looking for the side opposite the reference angle, which we will call x.  Therefore, the sin ratio is the one we need, as sin is equal to the side opposite over the hypotenuse.  $sin(75)= \frac{x}{150}$ and 150 sin(75) = x.  That gives you an x value of 144.89, first choice above.