Question

use pythagorean theorem to find the missing side of a right triangle
$a^2 + b^2 = c^2$
what is the length of the missing side of the triangles below?
(right triangle with legs 8, 15 and hypotenuse x; right triangle with leg 7, hypotenuse 18 and leg x)

Explanation:

Step1: Solve for the first triangle (with sides 8, 15, x)

The Pythagorean Theorem is \(a^2 + b^2 = c^2\), where \(a = 8\), \(b = 15\), and \(c = x\) (hypotenuse).
Substitute the values: \(8^2 + 15^2 = x^2\)
Calculate: \(64 + 225 = x^2\) → \(289 = x^2\)
Take the square root: \(x = \sqrt{289} = 17\)

Step2: Solve for the second triangle (with sides 7, 18, x)

Here, the hypotenuse is 18, one leg is 7, and the other leg is \(x\). Using the theorem \(a^2 + b^2 = c^2\), we can rearrange to \(b^2 = c^2 - a^2\) (where \(c = 18\), \(a = 7\), \(b = x\)).
Substitute: \(x^2 = 18^2 - 7^2\)
Calculate: \(x^2 = 324 - 49 = 275\)
Take the square root: \(x = \sqrt{275} = 5\sqrt{11} \approx 16.58\) (if we want a decimal approximation) or leave it as \(5\sqrt{11}\)

Answer:

For the first triangle (sides 8, 15, x): \(x = 17\)
For the second triangle (sides 7, 18, x): \(x = 5\sqrt{11}\) (or approximately \(16.58\))