Both are the angle between the line of sight and the horizontal, one looking up and one looking down. The word problems use any angle and a calculator; the figures use the special angles, so those answers stay exact.
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Pick more than one for a sheet that mixes them.
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The top of a building 30 feet tall is seen at an angle of elevation of 46∘. How far away is the observer, measured along the ground? Round to the nearest tenth.
A ramp has to rise 4 feet and make a 5∘ angle with the ground. How long is the ramp? Round to the nearest tenth.
From the top of a lighthouse 48 meters tall, the angle of depression to a boat is 32∘. How far is the boat from the base of the lighthouse? Round to the nearest tenth.
A pole 20 feet tall casts a shadow 47 feet long. What is the angle of elevation of the sun? Round to the nearest degree.
A plane flying at 3100 feet sees the start of a runway at an angle of depression of 7∘. How far is the plane from the runway, measured along its line of sight? Round to the nearest tenth.
A ramp 19 feet long rises 4 feet. What angle does it make with the ground? Round to the nearest degree.
A ramp has to rise 3 feet and make an 11∘ angle with the ground. How long is the ramp? Round to the nearest tenth.
A ramp 10 feet long rises 1 foot. What angle does it make with the ground? Round to the nearest degree.
From the top of a lighthouse 72 meters tall, the angle of depression to a boat is 5∘. How far is the boat from the base of the lighthouse? Round to the nearest tenth.
A ramp has to rise 4 feet and make a 12∘ angle with the ground. How long is the ramp? Round to the nearest tenth.
Find heights and lines of sight exactly
Find the height of the cliff. Give the exact answer.
Find the distance along the line of sight from the top of the cliff. Give the exact answer.
Find the distance along the line of sight to the top of the tower. Give the exact answer.
Find the height of the tower. Give the exact answer.
Find the height of the tower. Give the exact answer.
Find the height of the cliff. Give the exact answer.
Find the distance along the line of sight to the top of the tower. Give the exact answer.
Find the distance along the line of sight from the top of the cliff. Give the exact answer.
Find the height of the cliff. Give the exact answer.
Find the height of the tower. Give the exact answer.
Angles of Elevation and DepressionAnswer keyVersion 1
Date Period
Find each measure.
Solve elevation and depression problems
The top of a building 30 feet tall is seen at an angle of elevation of 46∘. How far away is the observer, measured along the ground? Round to the nearest tenth.29.0 ft
A ramp has to rise 4 feet and make a 5∘ angle with the ground. How long is the ramp? Round to the nearest tenth.45.9 ft
From the top of a lighthouse 48 meters tall, the angle of depression to a boat is 32∘. How far is the boat from the base of the lighthouse? Round to the nearest tenth.76.8 m
A pole 20 feet tall casts a shadow 47 feet long. What is the angle of elevation of the sun? Round to the nearest degree.23∘
A plane flying at 3100 feet sees the start of a runway at an angle of depression of 7∘. How far is the plane from the runway, measured along its line of sight? Round to the nearest tenth.25437.1 ft
A ramp 19 feet long rises 4 feet. What angle does it make with the ground? Round to the nearest degree.12∘
A ramp has to rise 3 feet and make an 11∘ angle with the ground. How long is the ramp? Round to the nearest tenth.15.7 ft
A ramp 10 feet long rises 1 foot. What angle does it make with the ground? Round to the nearest degree.6∘
From the top of a lighthouse 72 meters tall, the angle of depression to a boat is 5∘. How far is the boat from the base of the lighthouse? Round to the nearest tenth.823.0 m
A ramp has to rise 4 feet and make a 12∘ angle with the ground. How long is the ramp? Round to the nearest tenth.19.2 ft
Find heights and lines of sight exactly
Find the height of the cliff. Give the exact answer.253
Find the distance along the line of sight from the top of the cliff. Give the exact answer.182
Find the distance along the line of sight to the top of the tower. Give the exact answer.212
Find the height of the tower. Give the exact answer.183
Find the height of the tower. Give the exact answer.233
Find the height of the cliff. Give the exact answer.223
Find the distance along the line of sight to the top of the tower. Give the exact answer.252
Find the distance along the line of sight from the top of the cliff. Give the exact answer.202
Find the height of the cliff. Give the exact answer.203
Find the height of the tower. Give the exact answer.193
From 20 away the angle of elevation to the top of a tower is 45∘. Find its height
The height over the distance is the tangent of the angle.
tan 45 is 1.
The answer is 20.
Where students go wrong
Using the wrong ratio. Height and distance along the ground are the two legs, so they go with tangent. A ladder, a kite string or a line of sight is the hypotenuse, so that one goes with sine or cosine.
Also called angle of elevation, angle of depression or trigonometry word problems.
What you can put on this worksheet
Word problems, any angle, rounded
A 21-foot ladder leans against a wall and makes a 74∘ angle with the ground. How far is its foot from the wall? Round to the nearest tenth.→ 5.8 ft
Angles of elevation and depression
Find the height of the tower. Give the exact answer. — a right triangle with a elevation angle of 60°→ 93
Questions about these worksheets
Yes. Every angles of elevation and depression sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the angles of elevation and depression questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 2: word problems, any angle, rounded and angles of elevation and depression. Tick as many as you want and set how many of each, or let it spread them evenly.
Using the wrong ratio. Height and distance along the ground are the two legs, so they go with tangent. A ladder, a kite string or a line of sight is the hypotenuse, so that one goes with sine or cosine.