Pythagorean Theorem
What is the Pythagorean Theorem?
a2 + b2 = c2
Write the equation for the Pythagorean Theorem converse that would result in an acute triangle.
c2 < a2 + b2
In a 45-45-90 triangle, the legs are always ______ to each other.
Congruent
What is a cosine function?
adjacent over hypotenuse
Find the missing angle, given an adjacent side of 16 and a hypotenuse of 27. Round to the nearest tenth.
53.7
What is the hypotenuse in a triangle with side lengths of 10 and 7? Round to the nearest tenth.
12.2
Write the equation for the Pythagorean Theorem converse that would result in an obtuse triangle.
c2 > a2 + b2
In a 45-45-90 triangle, the leg is equal to 5, what is the hypotenuse?
5√2
Which function would you use, given an opposite side and adjacent side?
tangent
Find the missing angle, given an opposite side of 4 and hypotenuse of 19. Round to the nearest tenth.
12.2
What is the other side length of a triangle with side length of 16 and hypotenuse of 27? Round to the nearest tenth.
21.7
In a right triangle, c2 must be __________ compared to a2 + b2
equal
In a 30-60-90 triangle, the longer side is equal to 14√3. What is the hypotenuse?
28
Find the opposite side, given an angle of 34 degrees and hypotenuse of 20. Round to the nearest tenth.
11.2
The angle between the horizontal through the eye level and a line of sight to a point below eye level.
What is the angle of depression?
The side that is right across the 90 degree angle is called.
What is the hypothenuse?
What kind of triangle would result from side lengths, 10, 12, and 13?
Acute
In a 45-45-90 triangle, the hypotenuse is equal to 16. What is the leg equal to?
8√2
Find the hypotenuse, given the adjacent side of 17 and an angle of 54. Round to the nearest tenth.
28.9
The angle of elevation from a soccer ball on the ground to the top of the goal is 34 degrees. If the goal is 8 feet tall, what is the distance from the ball to the goal? Round to the nearest tenth.
11.9 ft
Scott is using a 12 foot ramp to load furniture into a truck. If the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck? Round to the nearest tenth.
11.5
What kind of triangle would result from side lengths of 12, 14 and 28?
Not a triangle!
In a 30-60-90 triangle, the hypotenuse is equal to 20√3, what is the length of the longer leg?
30
Max built a skateboarding ramp that is 16 inches high. The angle formed by the ramp and the ground is 21 degrees. What is the length of the ramp?
44.6
The angle of depression from the top of a cruise ship to the top of a sailboat is 22 degrees. Sitting above water, the cruise ship is 236 feet tall while the sailboat is 27 feet tall. Find the distance between the cruise ship and the sailboat. Round to the nearest tenth.
517.3 ft