Question

Find the unknown length in the right triangle with necessary approximate to the nearest thousandth. The answer choices are for 24, 4, 25,000

Answer 1

A right triangle is given and it is required that you find the unknown length.

Let the length of the unknown be x.

The right triangle is shown below:

Recall the Pythagorean Theorem which states that in a right triangle, the relationship between the lengths of legs a and b and the length of the hypotenuse, c is:

`a^2+b^2=c^2`

Substitute the side lengths provided into the equation:

`70^2+x^2=74^2`

Solve the resulting equation for x:

`\begin{gathered} \Rightarrow x^2=74^2-70^2 \\ \Rightarrow x^2=5476-4900=576 \\ \Rightarrow x^2=576 \\ \text{Take square root of both sides:} \\ \Rightarrow x=\sqrt[]{576}=24 \end{gathered}`

Hence, the required unknown length is 24 ft