eQuizShow

Right Triangles

Pythagorean Theorem

Question: Two legs of a right triangle measure 5 and 10. What is the length of the hypotenuse?
Answer: 5 times square root of 5

Question: Does a triangle with side lengths 9, 12, and 15 form a Pythagorean Triple?
Answer: Yes

Question: One leg of a right triangle is 11 inches. The hypotenuse is 61 inches. What is the length of the other leg?
Answer: 60 inches

Question: What type of triangle has side lengths 0.3, 0.4, and 0.6?
Answer: obtuse

Question: A painter leans a 15-ft ladder against a house. The base of the ladder is 5 ft from the house. To the nearest tenth of a foot, how high on the house does the ladder reach?
Answer: 14.1 ft

Special Right Triangles

Question: What is the relationship between the leg and hypotenuse in a 45-45-90 triangle?
Answer: The hypotenuse is square root of 2 times the leg.

Question: In a 30-60-90 triangle, what is the relationship between the hypotenuse and the short leg?
Answer: The hypotenuse equals 2 times the short leg.

Question: In a 30-60-90 triangle, what is the relationship between the long leg and the short leg?
Answer: The long leg equals square root of 3 times the shorter leg.

Question: In a 45-45-90 triangle, the length of the hypotenuse is 18. What is the length of each leg?
Answer: 9 times square root of 2

Question: In a 30-60-90 triangle, the length of the long leg is 15. What is the length of the hypotenuse and the length of the short leg?
Answer: hypotenuse = 10 times square root of 3
short leg = 5 times square root of 3

Trigonometry

Question: What does SOH - CAH - TOA stand for?
Answer: sine = opposite/hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite/adjacent

Question: In a right triangle, one of the angles measures 54 and the hypotenuse measures 17. What is the length of the side opposite the angle rounded to the nearest tenth?
Answer: 13.8

Question: In a right triangle, one of the angles measures 28 and the leg opposite that angle measures 1. What is the length of the leg adjacent to that angle, rounded to the nearest tenth?
Answer: 1.9

Question: In a right triangle, the measure of the side opposite angle X is 6 and the hypotenuse is 10. What is the measure of angle X to the nearest degree?
Answer: 37

Question: In a right triangle, the hypotenuse is 10 and the side adjacent to angle A is 8. Find the measure of angle A to the nearest degree.
Answer: 37

Angles of Elevation/Depression

Question: What type of angle (elevation or depression) is used based on the following description: A person standing on the ground looks up at the top of a ladder?
Answer: Angle of elevation

Question: What type of angle is described: An eagle in a tree spots a snake on the ground.
Answer: Angle of depression

Question: A fire ranger on a 150-ft tall tower spots a fire at a 30 degree angle of depression. How many feet away from the tower is the fire to the nearest tenth?
Answer: 259.8 ft

Question: A person can see the top of a building at an angle of 65 degrees. The person is standing 50 ft away from the building and has an eye level of 5 ft. How tall is the building to the nearest tenth of a foot?
Answer: 112.2 ft

Question: A wildlife biologist looks up at a 78 degree angle of elevation to see a flock of geese in the air. The biologist is standing 200 ft away from a place directly underneath the geese. How high are the geese flying to the nearest tenth of a foot?
Answer: 940.9 ft.

Random Geometry Questions

Question: One point on a number line is at -2 and another is at 7. What is the distance between these two points?
Answer: 9 units

Question: On a number line, there is a point at 10 and at -18. What is the midpoint of these points?
Answer: -4

Question: What is the distance between (-8, 4) and (4, -1)?
Answer: 13

Question: In a triangle, two of the angles measure 37 degrees and 89 degrees. What is the measure of the third angle?
Answer: 54

Question: Write the equation in slope-intercept form of the line that passes through the points (-2, 0) and (3, 10).
Answer: y = 2x + 4