Question

6. Find the length of the unknown side. Show work. Handwritten.
15 17

Answer 1

The length of the unknown side (base) in the right triangle is 8 units.

To find the length of the unknown side (base) in a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is 17 and the opposite side (also known as the height or altitude) is 15. Let's label the unknown side as 'x'.

Using the Pythagorean theorem, we can set up the equation:

`x^2 + 15^2 = 17^2`

Simplifying the equation:

`x^2 + 225 = 289`

Next, let's isolate the variable 'x' by subtracting 225 from both sides of the equation:

`x^2 = 289 - 225`

`x^2 = 64`

Now, to find the value of 'x', we take the square root of both sides of the equation:

`√((x^2)`= √64

x = 8

Therefore, the length of the unknown side (base) in the right triangle is 8 units.