# Angles of Elevation and Depression Word Problems Worksheet

One of the most common applications of right triangle trigonometry in the real-world are angles of elevation and depression word problems. That’s why I put together the best angles of elevation and depression word problems worksheet that you will ever find! I’ve also included a summary below of all the key information that you need to know in order to solve a given angle of elevation and depression word problem.

The best way to learn how to solve these word problems is by practicing! There are a variety of angles of elevation and depression word problems that you will encounter, so it is important to try many different problems. The worksheet I have developed will help you practice each type of problem that you will come across.

The worksheet can be found below!

## Angles of Depression Vs. Angles of Elevation

In order to solve angles of elevation and depression word problems, it is important to understand the difference between these two angles.

Imagine a tall building, and picture yourself standing at the top of the building looking out straight ahead along a horizontal line. We call this horizontal line the “line of sight”.

Just then, you hear someone call your name and you tilt your head from your line of sight downward. The angle formed between your line of sight and where your eyes are looking now is called the *angle of depression.*

Now imagine that you are the person who called up from ground level. If you tilt your head upward from your horizontal line of sight, the angle formed between your line of sight and where your eyes are looking now is the *angle of elevation.*

I recorded this video to demonstrate the difference between these two angles. It turns out taping a marker to your head and standing next to a whiteboard is a great way to see each angle in real-life!

## Solving Angles of Elevation and Depressions Problems

The first step to solve any angles of elevation and depression word problem is always to draw a diagram. These problems usually involve either an unknown horizontal distance or an unknown height to the top of a cliff or the height of a tower. Drawing a diagram will help you visually identify what exactly you are solving for in each problem.

Each problem will mention an angle of *elevation* of the top of an object or an angle of *depression* of the top of some object. After identifying the unknown, it is your job to determine any missing angles or missing side lengths! Having a good understanding of angle theorems is helpful when it comes to filling in any gaps in your diagram.

**Typically, a problem can be solved using the following process:**

- Draw a diagram.
- Identify the angle of elevation, angle of depression, and the unknown quantity.
- Use your understanding of alternate interior angles to determine any missing angles.
- Select one of the trigonometric ratios to help you solve for the missing side or missing angle.

## The Best Angles of Elevation and Depression Word Problems Worksheet

This is the best angles of elevation and depression word problems worksheet you will find! I have included 10 different types of word problems as well as their answers. This will allow you to check your answers to ensure you fully understand!

You will see examples that require you to calculate the height of the building and measure the distance to the base of the cliff. There are also specific problems that deal with calculating the height of the lamp post, the height of the tower, and other common measurements in the real-world.

**Download the worksheet by clicking below!**

## Review: Solving Angles of Depression and Angles of Elevation Real-World Problems

When it comes to solving a problem involving angles of depression or elevation, you will notice common themes. In general, it is always best to start with a diagram of the scenario. This will allow you to lay out the information given in order to make the best decision about the strategy to use. This is especially important when identifying which angle your are being given.

From there, you can rely on your understanding of the alternate angle theorem to fill in any missing angles. The final step will always be thinking about trigonometric ratios and how they can be used to solve for the value of the unknown.

I hope that you find this worksheet helpful as you practice solving these types of word problems! As a math teacher of many years, I was able to include a wide variety of problems that I used on tests in the past. These problems are designed to really challenge students to apply their understanding of angles of elevation and angles of depression to solve real-world problems.

Remember, the key to success in any studies of mathematics is regular practice!

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