# Lesson 10 Using Trigonometric Relationships Practice Understanding

## Learning Focus

Solve application problems using trigonometry.

How do I apply trigonometric ratios to practical problems?

What are the essential elements of modeling a real-world context using a right triangle, even when only an imaginary right triangle exists?

## Open Up the Math: Launch, Explore, Discuss

For each problem:

Make a drawing to represent the situation

Write an equation

Solve (do not forget to include units of measure)

### 1.

Carrie places a

### 2.

A flagpole casts a shadow that is

### 3.

In Southern California, there is a six-mile section of Interstate 5 that decreases

Pause and Reflect

### 4.

A hot air balloon is

### 5.

An airplane is descending as it approaches the airport. If the angle of depression from the plane to the ground is

### 6.

Michelle is

### 7.

A ramp is used for loading equipment from a dock to a ship. The ramp is

For each right triangle, find all unknown side lengths and angle measures:

### 8.

### 9.

### 10.

### 11.

### 12.

Draw and find the missing angle measures of the right triangle whose sides measure

Determine the values of the two remaining trigonometric ratios when given one of the trigonometric ratios. Also find the measures of the acute angles of the triangle.

### 13.

### 14.

### 15.

## Ready for More?

Compare and contrast two different methods for answering problems like those in problems 13–15.

Illustrate both of these methods to find

### 1.

One method is to create a “reference triangle” from the information given in the trigonometric ratio.

Given:

### 2.

A second method is to use the trigonometric identities developed in this unit, such as:

Using trigonometric identities:

## Takeaways

## Vocabulary

- model, mathematical
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we learned about the modeling process and how to use right triangle trigonometry to model many different types of applications, even applications that didn’t naturally include right triangles. A right triangle became a tool for representing a situation so we could draw upon trigonometric ratios and inverse trigonometric relationships to answer important problems in construction, aviation, transportation, and other contexts.

### 1.

Find the missing values for the similar right triangles.

### 2.

A doorstop, used as a wedge between the door and the floor to keep it open, is being designed with an angle of elevation of