Question

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.110Х14

Answer 1

From the picture, we can see that we have a right triangle. The hypontenuse (the side opposite to the right angle) is the side whose length of 14, where the side whise length is 11, and the one whose length is x, are the two hicks. We can establish the relationship of the Pythagoras theorem for this triangle:

`14^2=x^2+11^2`

We can solve for x:

`\begin{gathered} 14^2-11^2=x^2 \\ x^2=14^2-11^2 \\ x=\sqrt[]{14^2-11^2} \\ x=\sqrt[]{196-121} \\ x=\sqrt[]{75} \end{gathered}`

To find the square root of 75, we can decompose it:

75/5 = 15

15/5 = 3

3/3 = 1.

Then, 75 can be expressed the following way:

`75=5\cdot5\cdot3=5^2\cdot3`

Then:

`x=\sqrt[]{75}=\sqrt[]{5^2\cdot3}`

Since the square root of a product is the product of the square roots:

`\begin{gathered} x=\sqrt[]{5^2}\cdot\sqrt[]{3} \\ x=5\cdot\sqrt[]{3} \\ x\approx8.66 \end{gathered}`

The value of x is approximately 8.66,