Special Right Triangles
Pythagorean Theorem
Converse of the Pythagorean Theorem
Trig Functions
Angles of Elevation and Depression
100
What are the angle measures of the following triangle?
45-45-90
100
What is the equation for the Pythagorean Theorem?
a2 + b2 = c2
100
Can you form a triangle with the following side lengths?
4, 10, 6
Heck no.
100
What is cos J?
16/20
Bonus if you said 4/5
100
True or false.
An angle of depression occurs when you are looking down.
True
200
What is the value of x? Leave your answer as a radical.
34sqrt2
200
Find the value of a. Round to the nearest tenth, if necessary.
43.7
200
What kind of triangle is formed by the following side lengths?
13, 16, 17
acute
200
Find the value of x. Round to the nearest tenth.
25.4
200
A roofer props a ladder against a wall so the top of the ladder just reaches a 30-foot roof that needs repair. If the angle of elevation from the bottom of the ladder to the roof is 55°, how far is the ladder from the base of the wall? Round your answer to the nearest foot.
21 feet
300
Find the values of x and y. Leave your answer as a radical if necessary.
y=9
x=9sqrt3
300
Find the length of the diagonal. Round your answer to the nearest tenth.
18.4
300
The side lengths of a triangle are 12, 14, and x units. Find the possible values for x. Write your answer as an inequality.
2 < x < 26
300
A ladder is placed against a wall at a 40 degree angle. If they ladder is 12 feet long, how far away is the ladder from the base of the wall? Round your answer to the nearest tenth.
9.2 feet
300
From the top of the 120-foot-high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 19°. How far from the base of the tower is the airplane? Round to the nearest tenth of a foot.
348.5 feet
400
What is the value of x and y?
24/sqrt2 or 12sqrt2
400
A new television is listed as being 41 inches. This distance is the diagonal distance across the screen. If the height of the screen measures 20 inches, what is the width of the screen? Round to the nearest tenth of an inch.
35.8 in
400
Sasha is creating a garden that is shaped like a triangle. She is going to border the garden with a fence. If the longest side of the garden is 22 feet long and one of the shorter sides is 10 feet, what would the length of the third side need to be for the garden to be formed as a right triangle? Leave your answer in simplest radical form.
sqrt384
8sqrt6
400
Find WX, XZ, and angle W. Round to the nearest tenth.
WX= 15.1
XZ= 9.8
angle W= 33
400
Due to a storm, a pilot flying at an altitude of 528 feet has to land. If he has a horizontal distance of 2000 feet until he reaches the landing strip, what angle of depression should he use to land? Round to the nearest tenth of a degree.
14.8
500
Find the lengths of the triangle on this sail boat. Leave your answer as a radical.
hypotenuse:
30/sqrt3 or 10sqrt3
shorter leg:
15/sqrt3 or 5sqrt3
500
Construction workers are building a marble sidewalk around a park that is shaped like a right triangle. Each marble slab adds 2 feet to the length of the sidewalk. The workers find that exactly 1071 and 1840 slabs are required to make the sidewalks along the short sides of the park, not counting corner pieces. How many slabs are required to make the sidewalk that runs along the long side of the park?
2129 feet
500
Which of the following are side lengths to a right triangle? Select all that apply.
A. 2, 3, 4
B. 6, 8, 10
C. 12, 13, 15
D. sqrt(3), sqrt(4), sqrt(7)
B and D
500
The hypotenuse of a right triangle is 22 units. If one of the acute angles is 35 degrees, what are the lengths of the two legs? Round your answers to the nearest tenth.
longer leg: 18
shorter leg: 12.6
500
On a mountain bike trip along the Gemini Bridges Trail in Moab, Utah, Chloe stopped on the canyon floor to get a good view of the twin sandstone bridges. Chloe is standing about 60 meters from the base of the canyon cliff, and the natural arch bridges are about 100 meters up the canyon wall. If her line of sight is 5 meters above the ground, what is the angle of elevation to the top of the bridges? Round to the nearest tenth of a degree.
57.7