Pythagorean Theorem Quiz

In a right triangle, which side is always the longest?

If a triangle has angles measuring 60° and 30°, what type of triangle is it?

If the legs of a right triangle are 3 and x and the hypotenuse is 5, what is the value of x?

What is the rise of a road with a 7% grade for a run of 100ft?

What is the length of a ladder needed to reach a window 12 ft above ground using a 4:1 vertical to horizontal ratio?

For a triangle with sides of lengths 1, 2, and 3, which statement is correct?

What is the relationship between the angles and sides in any triangle?

In a right triangle, if one angle is 70°, what can be said about the other two angles?

Pythagorean Theorem

A 90° angle is a right angle.
A right triangle has a 90° angle.
The side opposite the 90° angle is the hypotenuse.
The other two sides are the legs.
The angles in any triangle add up to 180°.
The longest side is opposite the largest angle; the shortest side is opposite the smallest angle.
In a right triangle, the hypotenuse is the longest side.
a² = b² + c² (formula relating sides of a right triangle)

Exercise 1

Question 1: Given angles 60° and 30° in a triangle, is it a right triangle? No.
Question 2: A triangle with a 100° angle is it a right triangle? No.
Question 3: A triangle with a 70° angle is it a right triangle? Maybe.
Question 4: Legs of a right triangle are 3 and x, hypotenuse is 5. Find x. x = 4
Question 5: Triangle side lengths 1, 3, and 2. Is it a right triangle? No.

Exercise 2

Question 1: A 12 ft high window, 4:1 vertical to horizontal ratio for a ladder. What is the length of the ladder? 12.37 ft
Question 2: Triangle with sides A,B, and C (C=19, A=x, B=3x). Find A and B. A=6.01, B=18.03
Question 3: (Figure with iterative side lengths). Find X6. X6 = 2.65
Question 4: A 3 ft high truck bed ramp with a 25% grade. How long is the ramp? 12.37 ft

Test your knowledge of the Pythagorean Theorem and right triangles. This quiz covers fundamental properties, angles, and calculations associated with right triangles. Challenge yourself with a series of questions that reinforce your understanding of this important geometric concept.