Special Right Triangles Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A 45-45-90 triangle has legs of length 7. Find the length of the hypotenuse.

Solution

  1. 1
    Step 1: Recall the 45-45-90 ratio: if each leg has length aa, the hypotenuse has length a2a\sqrt{2}.
  2. 2
    Step 2: The legs are both 7, so a=7a = 7.
  3. 3
    Step 3: Hypotenuse =72≈7×1.414=9.9= 7\sqrt{2} \approx 7 \times 1.414 = 9.9.

Answer

Hypotenuse =72≈9.9= 7\sqrt{2} \approx 9.9.
In a 45-45-90 triangle, the two legs are equal and the hypotenuse is 2\sqrt{2} times the length of a leg. This ratio (1:1:21:1:\sqrt{2}) comes from applying the Pythagorean theorem: a2+a2=c2a^2 + a^2 = c^2, so c=a2c = a\sqrt{2}.

About Special Right Triangles

Two families of right triangles whose side ratios can be determined exactly: the 30-60-90 triangle with sides in ratio 1:3:21 : \sqrt{3} : 2, and the 45-45-90 triangle with sides in ratio 1:1:21 : 1 : \sqrt{2}.

Learn more about Special Right Triangles →

More Special Right Triangles Examples

Example 2 medium

In a 30-60-90 triangle, the hypotenuse is 16. Find the lengths of both legs.

Example 3 easy

The diagonal of a square is 10 cm. Find the side length of the square.

Example 4 hard

An equilateral triangle has side length 12. Find its height and area using the 30-60-90 triangle rel

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