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Angle of Elevation and Depression Trig Word Problems - Printable Mathematics Worksheets - Wayground

Angle of Elevation and Depression Trig Word Problems

9 questions

7th - 11th Grade

Mathematics

Angle of Elevation and Depression Trig Word Problems is a free printable mathematics worksheet for students in Grades 7–11. It contains nine fill-in-the-blank problems that use right-triangle trigonometry to find heights, horizontal distances, slant distances, and required angles in real-world situations involving kites, airplanes, ships, flagpoles, cliffs, buildings, and ladders. Students must interpret each scenario, identify the known and unknown sides or angle, select an appropriate trigonometric relationship, and calculate a numerical answer. The problems include both angles of elevation and angles of depression, as well as cases where students must distinguish between vertical height, horizontal distance, and the hypotenuse. A complete answer key supports checking work and reviewing calculation methods. This worksheet is available as a free printable PDF and is also useful for digital practice on Wayground.

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Worksheets

Angle of Elevation and Depression Trig Word Problems

Total questions: 9

Name
Class
Date
1.

Brian’s kite is flying above a field at the end of 65 m of string. If the angle of elevation to the kite measures 70°, how high is the kite above Brian’s head? (Assuming he is holding the end of the string by his head)

(a)  

2.

From an airplane at an altitude of 1200 m, the angle of depression to a building on the ground measures 28°. Find the distance from the plane to the building.

(a)  

3.

From a point on the ground 12 ft from the base of a flagpole, the angle of elevation of the top of the pole measures 53°. How tall is the flagpole?

(a)  

4.

From a plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35° and 25°. How far apart are the ships?

(a)  

5.

A man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52° . How high off the ground is the kite?

(a)  

6.

A man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52° . How far away is the man from the spot directly under the kite?

(a)  

7.

From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º. How far is the object from the base of the cliff?

(a)  

8.

An airplane takes off 200 feet in front of a 60 foot building. At what angle of elevation must the plane take off in order to avoid crashing into the building? Assume that the airplane flies in a straight line and the angle of elevation remains constant until the airplane flies over the building.

(a)  

9.

A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in order to reach the top of the wall?

(a)  

Answer Key

Angle of Elevation and Depression Trig Word Problems

Total questions: 9

1.
61.1
2.
2556.1
3.
15.9
4.
189.8
5.
78.8
6.
61.6
7.
59.3
8.
17, 16.7
9.
68, 68.2

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FAQs

What does the Angle of Elevation and Depression Trig Word Problems worksheet cover?

This worksheet covers solving nine fill-in-the-blank right-triangle word problems involving angles of elevation and depression. Students use trigonometric ratios to find unknown heights, horizontal distances, slant distances, and angles in situations such as kite strings, aircraft, ships, cliffs, buildings, and ladders.

How can I use this worksheet to teach angles of elevation and depression?

Begin by having students sketch a right triangle for each scenario and label the vertical, horizontal, and slanted measurements before choosing a trigonometric ratio. Use the kite and airplane items to discuss how an angle of elevation is measured upward from a horizontal line, while an angle of depression is measured downward from a horizontal line; then have students explain which distance the fill-in response represents.

What mistakes should I watch for when students complete this trigonometry worksheet?

Students may confuse the hypotenuse, opposite side, and adjacent side, causing them to select the wrong trigonometric ratio. Watch for students treating an angle of depression as if it changes the triangle, solving for the kite's horizontal distance when the question asks for its height, or rounding too early. They should also check that their calculators are set to degree mode.

How do I assign and grade this Angle of Elevation and Depression worksheet?

You can assign this worksheet as a printable PDF or use it as a digital quiz on Wayground. It includes a complete answer key for checking the nine numerical responses, and printable student work can be graded by scanning it with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time.

How can I differentiate this worksheet for my students?

In the worksheet's Advanced Settings, adjust font spacing or increase the font size so the nine fill-in-the-blank trigonometry problems have more room for reading and working. You can also enable a dyslexia-friendly font or translate the worksheet into another language to make the scenario-based questions easier to access.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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