Question

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

Answer 1

Using the Pythagorean Theorem with a hypotenuse of 10 and a height of 8, the side length x in the right triangle is found to be 6 units when rounded to the nearest hundredth.

To find the side length x in the right triangle, you can use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the other two sides a and b:

`\[ c^2 = a^2 + b^2 \]`

In this case, the hypotenuse c is given as 10, and the height a is given as 8. Substitute these values into the equation:

`\[ 10^2 = 8^2 + x^2 \]`

Solving for x:

`\[ 100 = 64 + x^2 \]\\\x^2 = 36 \]\\\ x = √(36) \]`

x = 6

So, the side length x is 6.

Answer 2

x = 6

Explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, then

x² + 8² = 10²

x² + 64 = 100 ( subtract 64 from both sides )

x² = 36 ( take square root of both sides )

x =
`√(36)` = 6