Right Triangle Similarity
Pythagorean Theorem
Special Right Triangles
Trigonometric Ratios
Angles of Elevation & Depression
100
Two triangles are similar. The Triangle A has legs 3 cm and 4 cm, Triangle B has legs 6 cm and 8 cm. The length of the hypotenuse of Triangle B is
What 10 cm?
100
Find the length of the hypotenuse of a right triangle if the legs are 4 and 6. Express your answer is reduced radical form.
What is 2 times the square root of 13?
100
In a 30-60-90 triangle, the hypotenuse has length 14. Find the length of the two legs.
What is 7 and 7 square roots of 3.
100
The legs of a right triangle have length x and 20. The acute angle adjacent to the 20 side is 35 degrees. Find x.
What is 14.
100
The pilot of a plane flying at an altitude of 1000' looks down at a traffic control personel on the groud. The angle of depression is 25 degrees. What is the distance from the plane to the control personnel?
What is 2,366.3 ft.
200
Mrs. Smith is trying to determine the height of a tree. She is 5 feet tall and her shadow is 15 feet long. The shadow of the tree is 39 feet long. Give the height of the tree.
What 13 feet tall?
200
The length of a rectangular painting is 3" longer than its width. If the diagonal is 15" long, what are the dimensions of the painting?
What is 9" x 12".
200
An isosceles right triangle has a leg of length 4 times the square root of 2. Find the length of the hypotenuse.
What is 8.
200
The leg of a right triangle has length 2.7 and the hypotenuse has length x. The acute angle adjacent to the 2.7 side is 57 degrees. Find x.
What is 4.96 = 5.
200
A man is standing at the foot of a hill. He looks up the hill and sights a spot that is 35ft from where he is. The mans eyes are 5'10" from the ground. What is the measure of the angle of elevation of the hill?
What is 10 degrees.
300
Two buildings are across the street from each other. The tallest building is 675 feet tall and is 50 feet from the curb. The smaller building is 20 feet from the curb. Give the height of the smaller building.
What 270 feet tall?
300
James has a circular trampoline with a diameter of 16 feet. Explain why this trampoline will or will not fit through the door.
It will not because the diagonal of the door is 11.66 feet which is smaller than 16 feet, the diameter of the trampoline.
300
in a 45-45-90 triangle, the hypotenuse has length 8. Find the length of the legs.
What is 4 times the square root of 2.
300
The diagonal of a rectangle is 100". It separates the right angles into 40 and 50 degrees. Find the length and width of the rectangle.
What is 76.6" and 64.3".
300
A ranger is at the top of a 200ft lookout tower. She spots a fire at an angle of depression of 3 degrees from the top of her tower. How far away is the tower?
What is 3817 ft.
400
Triangle A measures 39, 52, and 65. Triangle B is similar to Triangle A and its smallest leg measures 42. Give the hypotenuse of Triangle B.
What is 70?
400
For safety reasons, the base of a ladder that is 24 feet tall should be at least 8 feet from the wall. What is the highest distance that the 24 foot ladder can safely rest on the wall?
What is 22.63 feet
400
in a 30-60-90 triangle, the longer leg has a length of 36. Find the length of the shorter leg and the hypotenuse.
What is 12 times the square root of 3 (shorter leg) and 24 times the square root of 3 (hypotenuse).
400
Each base angle of an isosceles triangle measures 50 degrees. The altitude to the base is 26cm long. Find the length of the base.
What is 44cm.
400
From a lighthouse 1000ft above sea level, the angle of depression to a boat is 29 degrees. One minute later the boat has traveled toward the lighthouse and is now at a 44 degree angle of depression from the light house. How far to the nearest foot did the boat travel in that minute?
What is 769 ft.
500
Two sides of an open tent are 13 feet long. The distance from the center pole to one side is 12 feet. Give the height of the pole.
What is 5 feet.
500
The length of the hypotenuse of a right triangle is 26cm. One leg is 14cm longer than the other. Find the length of each leg.
What is 10cm and 24cm.
500
Find the perimeter of an equilateral triangle with an altitude of 6 times the square root of 3 inches.
What is 36".
500
The base of an isosceles triangle is 12cm long. Its vertex angle is 70 degrees. Find the length of each congruent side.
What is 10.5 cm.
500
Jillian knows that when she stands 134 ft from the base of a flagpole, the angle of elevation to the top of the flagpole is 27°. If her eyes are 5.3 ft from the ground, find the height of the flagpole.
What is 73.6 feet
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