Question

Find the length of the missing side of the right triangle.

Answer 1

39 units

Explanation:

Since two side lengths and a right angle are given, we can use pythogoras theorem to determine the missing side (c) of the triangle. It should be noted that pythgoras theorem can only be used if the triangle is a right triangle.

Pythogoras theorem formula:

`(\text{Side}_(1) })^(2) + (\text{Side}_(2) )^(2) = (\text{Hyptenuse})^(2)`

Substitute the legs of the triangle and the hyptenuse

`\implies (36)^(2) + (15 )^(2) = (c)^(2)`

Simplify both sides of the equation

`\implies 1296 + 225 = (c)^(2)\\`

`\implies 1521 = (c)^(2)\\`

Take square root both sides

`\implies \sqrt[2]{1521 } = \sqrt[2]{c^(2) }`

Solve for "c" by simplifying the roots

`\implies \sqrt[2]{39 * 39 } = \sqrt[2]{c * c }`

`\implies \boxed{39 = c}`

Thus, the measure of the missing side length (c) is 39 units.