The altitude drawn to the hypotenuse of a right triangle is the geometric mean of these two segments.
What is hyp1 and hyp2 (the two pieces of hypotenuse).
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 square roots 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 personel?
What is 2,366.3 ft.
200
The altitude to the hypotenuse of a right triangle has length 2cm. If it seperates the hypotenuse into 4cm and 1cm, find the lengths of both legs.
What is sq. root 5 and two sq. roots of 5.
200
The length of a rectanglular 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 square roots 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
In a right triangle, the altitude to a 6 ft. hypotenuse bisects teh hypotenuse. Find the length of the altitude and each leg.
What is 3 ft. (alt), and 3 square roots of 2 ft. (legs).
300
A storage space is 12' x 4' with walls 3' high. Find the distance from the top back left corner, to the bottom front right corner (opposite corners of the space).
What is 13'.
300
in a 45-45-90 triangle, the hypotenuse has length 8. Find the length of the legs.
What is 4 square roots of 2.
300
The diagonal of a rectangle is 100". It seperates 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
Find the length of the altitude to the hypotenuse of a right triangle whose legs and hypotenuse measure 3, 4 and 5, respectively.
What is 12/5 = 2.4 .
400
ABCD is a rhombus with side lengths of 8. For what value of AC will ABCD be a square? Express your answer in reduced radical form.
What is 8 square roots of 2.
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 square roots of 3 (shorter leg) and 24 square roots 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 form a 90 degree angle at the peak. An 8-ft support pole from the peak, placed at a 90 degree angle with the ground, divides the ground line in a 1-to-4 ratio. Find the length of the ground line.
What is 20 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 square roots 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
The diagonals of a rhombus measure 10cm and 24cm. To the nearest degree, find the measures of the angles of the rhombus.