Pythagorean Theorem
Converse of Pythagorean Theorem
Special Right Triangles
Trigonometry
Angle of Elevation & Depression
100
If a triangle has side lengths of 56, 90, and 106, then determine which number correlates to the legs and hypotenuse.
What is leg, leg, and hypotenuse?
100
Determine if the lengths form a right triangle. 514, 684, and 855.
What is No?
100
Use your knowledge of a 45-45-90 right triangle to find the missing variable in the triangle.
What is 28 radical 2 or 28 square root of 2?
100
What is the trigonometric ratios for sine, cosine, and tangent.
What is opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent?
100
The angle formed by an observer's line of sight and a horizontal line, when looking up to an object.
What is angle of elevation?
200
Do the following side lengths form a Pythagorean Triple? 11, 12, and 15
What is No?
11^2 + 12^2 = 15^2
121 + 144 = 225
265 does not equal 225
No, these side lengths do not form a Pythagorean Triple
200
Determine if the lengths form a right triangle. 450, 1080, and 1170.
What is Yes?
200
Determine the value of the missing sides for the following triangle. Your answer must be written in radical form.
What is 7 and 7 radical 3?
200
Consider the figure below and determine the value of sine, cosine, and tangent of <G.
What is 700/821, 429/821, and 700/429?
200
The angle formed by an observer's line of sight and a horizontal line, when looking down to an object.
What is angle of depression?
300
Alice leaves her house and walks to school. She walks 45 meters south and 336 meters east. How far is Alice from her house?
What is 339?
300
Given the following side lengths, determine if the triangle is an acute, right, or obtuse triangle. 11, 12, and 15
What is acute?
300
Use your knowledge of a 45-45-90 right triangle to find the missing variable in the triangle.
What is 23 radical 2 over/divided by 2?
300
Determine the unknown values , R and W, in the figure below.
What is 15.6 and 28.6?
300
A straight road to the top of a mountain is 25,525 feet long and makes a 44 degrees angle of elevation from sea level. Determine the height of the mountain.
What is 17,731.15?
400
If the hypotenuse of a right triangle is 125 units long and the short leg adjacent to the right angle is 32 units long, determine the length of the long leg of the triangle.
What is 120.8?
400
Given the following side lengths, determine if the triangle is an acute, right, or obtuse triangle.
What is obtuse?
400
What is the ratio of the short leg to the long leg in a 30-60-90 triangle?
What is
400
Using what you know about trigonometric functions, determine the angle measure of <S and <F.
What is 67.4 degrees and 22.6 degrees?
400
Airplanes use Distance Measuring Equipment (DME) to measure the distance from the plane to a nearest radar station. If the distance from a plane to a radar station is 160 miles and the angle of depression is 34 degrees, find the number of ground miles from a point directly below the plane to the radar station.
What is 132.65 units?
500
The walls of square storage room in a warehouse are 300 feet long. What is the distance from one corner to the other corner of the storage room?
What is 424 feet?
500
Determine if the triangle on the coordinate plane is a right triangle by using the Converse of Pythagorean theorem.
What is No?
500
The length of the side opposite the 30 degree angle of a 30-60-90 triangle is 323 ft. Determine the length of the other two sides. Both answers must be rounded to the nearest tenth or hundredth place.
What is 559.5 feet and 646 feet?
500
A right triangle has a hypotenuse of length 59 and one leg of length 23. Determine the angle measure of the other two acute angles in the triangle and the side length of the other leg. Round to the nearest hundredth.
What is 67.06 degrees, 22.94 degrees, and 54.33?
500
At the museum, there is a Jack in the Beanstalk play area with stairs and a slide representing Jack’s journey up to the giant’s lair. Consider the diagram of the play area below.
Each step is two feet long and three feet high. If Jack is standing 4 feet from the base of the stairs, determine the angle of elevation from the ground where Jack is standing to the top of the stairs. Round your answer to the nearest tenth of a degree.
What is 46.97 degrees?
