A loading ramp 10 feet long that makes an angle of 18^∘ with the horizontal is to be replaced by

Name: Problem 44, Chapter 7: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2021-06-28T21:11:09-08:00
Duration: 1 min 55 s
Channel: Sheryl Ezze
Description: A loading ramp 10 feet long that makes an angle of 18^∘ with the horizontal is to be replaced by a ramp that makes an angle of 12^∘ with the horizontal. How long is the new ramp?

step 1 We know we have a loading dock ramp and we know that it is 10 feet long and we know that it is a

Question

A loading ramp 10 feet long that makes an angle of $18^{\circ}$ with the horizontal is to be replaced by a ramp that makes an angle of $12^{\circ}$ with the horizontal. How long is the new ramp?

   A loading ramp 10 feet long that makes an angle of $18^{\circ}$ with the horizontal is to be replaced by a ramp that makes an angle of $12^{\circ}$ with the horizontal. How long is the new ramp?

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan,… 3rd Edition

Chapter 7, Problem 44

Instant Answer

Solved by Expert Sheryl Ezze

06/28/2021

Step 1

We can use the sine function to find the height of the ramp. The sine function is defined as the ratio of the length of the side that is opposite the angle to the length of the hypotenuse. In this case, the hypotenuse is the length of the ramp and the opposite Show more…

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A loading ramp 10 feet long that makes an angle of $18^{\circ}$ with the horizontal is to be replaced by a ramp that makes an angle of $12^{\circ}$ with the horizontal. How long is the new ramp?

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Key Concepts

Trigonometric Functions (Sine)

The sine function relates an angle in a right triangle to the ratio of the length of the side opposite that angle to the hypotenuse. In problems involving ramps or inclines, the sine function is used to calculate the vertical height given the ramp length and angle of inclination, or vice versa, allowing one to solve for unknown dimensions when the angle changes.

Right Triangle Geometry

This concept involves understanding the relationships between the angles and sides of a right triangle. In many real-world problems, such as determining the dimensions of a loading ramp, the ramp can be modeled as the hypotenuse of a right triangle where one leg represents the vertical height and the other leg represents the horizontal distance.

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