In these lessons, we will learn
A 45-45-90 triangle is a special right triangle whose angles are 45º, 45º and 90º.
The lengths of the sides of a 45º-45º-90º triangle are in the ratio of
1:1:√2.
The following diagram shows a 45-45-90 triangle and the ratio of its sides. Scroll down the page for more examples and solutions.
A right triangle with two sides of equal lengths is a 45°-45°-90° triangle.
You can also recognize a 45°-45°-90° triangle by the angles. As long as you know that one of the angles in the right-angle triangle is 45° then it must be a 45°-45°-90° special right triangle.
A right triangle with a 45° angle must be a 45°-45°-90° special right triangle.
Example 1:
Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are both 3 inches.
Solution:
Step 1: This is a right triangle with two equal sides so it must be a 45°-45°-90° triangle.
Step 2:
You are given that the both the sides are 3. If the first and second
value of the ratio
is 3 then the length of the third side is
Answer: The
length of the hypotenuse is
inches.
Example 2:
Find
the lengths of the other two sides of a right triangle if the length
of the hypotenuse is
inches and one of the angles is 45°.
Solution:
Step 1: This is a right triangle with a 45° so it must be a 45°-45°-90° triangle.
Step 2: You are given that the hypotenuse is
. If the third value of the ratio
is
then the lengths of the other two sides must 4.
Answer: The lengths of the two sides are both 4 inches.
The following videos show more examples of 45-45-90 triangles.
How to find the length of a leg or hypotenuse in a 45-45-90 triangle using the Pythagorean Theorem and then derive the ratio between the length of a leg and the hypotenuse?Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
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