A set of three positive integers a, b, and c that satisfy the equation c squared = a squared + b squared.
What is Pythagorean Triple?
100
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the square of the length of the legs.
What is Theorem 7.1- Pythagorean Theorem?
100
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
What is Theorem 7.2- Converse of Pythagorean Theorem?
100
In a right triangle, if the legs equal 6 and 10, find the hypotenuse using the Pythagorean Theorem. (Round to the 3rd decimal if necessary)
The hypotenuse equals 11.662.
100
In a triangle, one leg equals 12, the other leg equals 2x, and the last leg equals 20. Solve for the value of x.
X=8
200
A ratio of the lengths of two sides of a right triangle.
What is Trigonometric Ratio?
200
In a 45-45-90 degree triangle, the hypotenuse is the square root of 2 times as long as each leg.
What is Theorem 7.8- 45-45-90 Triangle Theorem?
200
The angle your line of sight makes with a horizontal line when you look up at an object.
What is Angle of Elevation?
200
A triangle has side lengths of 6, 8, and 9. Tell whether the triangle is Obtuse, Right, or Acute.
The triangle is Acute.
200
5, 15, x. Solve for the value of x to make the triangle a right triangle. (Round to the nearest tenth)
X=15.8
300
To find the measure of all the sides and angles of a right triangle.
What is Solve a Right Triangle?
300
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the two other sides, than the triangle is an obtuse triangle.
What is Theorem 7.4?
300
In a 30-60-90 degree triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of 3 times as long as the shorter leg.
What is Theorem 7.9- 30-60-90 Triangle Theorem?
300
In a 45-45-90 degree triangle, if the a leg equals 7, what does the hypotenuse equal. (Round to the 3rd decimal if necessary)
The hypotenuse equals 9.899.
300
In a 30-60-90 triangle, the shortest leg equals 8 and the longest leg equals 8x. Solve for the value of x. (Round to the nearest tenth)
X=1.7
400
Trigonometric ratio for acute angles that is length of adjacent leg over length of hypotenuse.
What is Cosine?
400
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.
What is Theorem 7.6- Geometric Mean (Altitude) Theorem?
400
In triangle ABC, the hypotenuse equals 9, one leg equals 5, and the other leg equals 6x. Solve for the value of x. (Round to the nearest tenth)
X=7.5
400
In triangle BEN, if segment BE=6 and segment NB=9. Find the measure of angle B is the hypotenuse is NB. (Round to the nearest tenth)
Angle B=48.2
400
In triangle ABC, angle B=36 degrees, segment AB=7, and segment BC=x. Solve for the value of x if AB is the hypotenuse. (Round to the nearest tenth)
X=5.7
500
The ratio of the lengths of the legs in a right triangle, length of opposite leg over length of adjacent leg.
What is Tangent?
500
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
What is Theorem 7.5?
500
The length of the slope of one side of a hill in your neighborhood 200 feet. The height of the hill is 75. What is the angle of elevation of the hill? (Round to the nearest tenth)
The angle of elevation is 22.0 feet tall.
500
A 23 foot string is attached to the top of a flagpole and too the ground 15 feet away from the flagpole. What is the height of the flagpole? (Round to the nearest tenth)
The flagpole is 17.4 feet tall.
500
In a 45-45-90 triangle, the tangent of both 45 degree angles equals 1/2x. Solve for the value of x.