30-60-90 Triangles Basics
In a 30-60-90 triangle, if the shortest side is x, what is the length of the hypotenuse?
What is 2x?
In a 45-45-90 triangle, if each leg measures 4, find the hypotenuse.
What is 4√2?
In a 45-45-90 triangle with legs of length x, express the hypotenuse in terms of x using the Pythagorean Theorem.
What is x√2?
Find the length of the leg of an isosceles right triangle if the hypotenuse measures 6√2.
What is 6?
Calculate the height of an equilateral triangle with side length 6 using special triangles.
What is 3√3?
In a 30-60-90 triangle, if the shortest side is 5, what is the length of the longer leg?
What is 5√3?
A 45-45-90 triangle has a hypotenuse of 10. What is the length of each leg?
What is 5√2?
For a 30-60-90 triangle with a smallest side of x, use Pythagorean Theorem to find the hypotenuse.
What is 2x?
Calculate the angle in degrees formed between a diagonal and a side of a square.
What is 45°?
If a ladder forms a 30° angle with the ground and reaches a height of 10 feet on a wall, how long is the ladder?
What is 20 feet?
If the side opposite the 60° angle is 9√3, what is the length of the shortest side in a 30-60-90 triangle?
What is 9?
Find the area of a 45-45-90 triangle if each leg measures 6.
What is 18?
In a 30-60-90 triangle with a smallest side of length 4, find the area of the triangle using the special triangles properties.
What is 8√3?
Explain why a 45-45-90 triangle is sometimes called an isosceles right triangle.
What is because it has two equal sides and a 90° angle?
A surveillance camera is mounted on a wall and forms a 45° angle with the ceiling. If the hypotenuse of the triangle formed is 10 meters, find the distance from the camera to the ceiling.
What is 5√2 meters?
Given a 30-60-90 triangle where the length of the hypotenuse is 12, what is the length of the side opposite the 60° angle?
What is 6√3?
The perimeter of a 45-45-90 triangle is 24 + 12√2. Find the length of one leg.
What is 8?
Using the Pythagorean Theorem, find the hypotenuse of a 30-60-90 triangle if the longer leg is 9 units.
What is 18?
If the leg of a 45-45-90 triangle is x, write an equation relating the hypotenuse and the leg.
What is hypotenuse = x√2?
An architect is designing a stairway with each step making a 45° angle with the floor. If the height from floor to ceiling is 10 feet, what should be the length of each step's hypotenuse?
What is 10√2 feet?
A 30-60-90 triangle has a side of length 8 opposite the 60° angle. Calculate the length of the hypotenuse.
What is 16?
If the hypotenuse of a 45-45-90 triangle is 14, calculate the area of the triangle.
What is 49?
In a 45-45-90 triangle, if the leg measures 5√2, calculate the perimeter of the triangle.
What is 15 + 5√2?
Calculate the diagonal length of a square with side lengths of 8 using properties of special triangles.
What is 8√2?
A ramp rises 12 meters horizontally at a 30° incline. Calculate the length of the ramp using properties of special triangles.
What is 24 meters?