Pythagorean Theorem
A right triangle has one leg that is 7 units long and another that is 24 units long. what is the length of the hypotenuse.
c=25 units
In a right triangle, if the angle opposite to the side you're measuring is 30 degrees and the hypotenuse is 10 units long, what is the length of the opposite side?
5 units
find the length of the adjacent side in a right triangle if the angle is 60 degrees and the hypotenuse is 12 units.
6 units long
In a right triangle, if the angle is 30 degrees and the adjacent side is 4 units long, what is the length of the opposite side?
2.31 units long
In a triangle, if two sides are 5 units and 7 units long, and the included angle is 60 degrees, what is the length of the third side?
8.66 units
The hypotenuse of a right triangle is 10 units long, and one of the legs is 6 units long. How long is the other leg?
b=8 units
Calculate the height of a tree if you stand 30 meters away from it and the angle of elevation from your point to the top of the tree is 45 degrees.
30 meters
A ladder is leaning against a wall, making a 75- degree angle with the ground. If the ladder is 20 feet long, how far is it from the wall?
5.18 ft from the wall
A flagpole casts a shadow of 15 meters when the angle of elevation of the sun is 60 degrees. How tall is the flagpole?
25.98 meters tall
A rectangle has a length of 10 units and a diagonal of 13 units. What is the measure of one of the angles in the rectangle?
30 degrees
Find the length of the hypotenuse if the legs of a right triangle measure 9 units and 12 units.
c= 15 units
A ramp is inclined at an angle of 20 degrees to the horizontal. If the ramp is 50 meters long, how high does it reach?
17.32 meters
Determine the width of a river if you can measure an angle of 45 degrees from one bank to a tree directly across on the other bank, and you are standing 100 meters from the tree.
100 meters
From a distance of 20 meters, you measure the angle of elevation to the top of a tree as 45 degrees. How tall is the tree?
20 meters tall
In a trapezoid, the bases are 8 units and 12 units long, and one of the legs is 6 units long. What is the length of the other leg?
A ladder leans against a wall, forming a right angle with the ground. If the ladder is 15 units long and reaches 9 units up the wall, how far is the base of the ladder from the wall?
A=12 units
If the sine of an angle in a right triangle is 0.6 and the length of the hypotenuse is 5 units, what is the length of the opposite side?
3 units
If the cosine of an angle in a right triangle is 0.8 and the adjacent side is 8 units long, what is the length of the hypotenuse?
10 units long
If the tangent of an angle in a right triangle is 0.75 and the opposite side is 5 units long, what is the length of the adjacent side?
6.67 units
In a parallelogram, one angle, measures 45 degrees. What are the measures of the other three angles in the parallelogram?
1. 135 degrees
2. 45 degrees
3. 135 degrees
In a right angles triangle, the lengths of the legs are 8 units and 15 units. Determine the length of the hypotenuse.
c= 17 units
You are flying a kite and the string makes an angle of 55 degrees with the ground. If you have let out 100 meters of string, how high above ground is the kite?
82.92 meters
You're at the top of a lighthouse and looking at a boat in the water, creating a 30 degree angle with your line of sight down to the boat. If the lighthouse is 50 meters tall, how far is the boat from the base of the lighthouse?
86.60 meters
You're standing on a hill and looking down at a river. The angle of depression to the river is 40 degrees, and you're 100 meters above the river. How far away is the river horizontally?
83.91 meters
A circle has a radius of 5 units. If a central angle measures 60 degrees, what is the length of the corresponding arc?
5.24 units