Question

Find the missing side of the triangle.A. 19−−√ miB. 22–√ miC. 11−−√ miD. 1 mi

Answer 1

From the right angled triangle given,

To find the missing side, x, of the triangle, Pythagorean theorem is applied

The Pythagorean theorem formula is

`\begin{gathered} (\text{Hyp)}^2=(\text{Opp)}^2+(\text{Adj)}^2 \\ \text{Hyp is the hypotenuse} \\ \text{Opp is the opposite } \\ \text{Adj is the adjacent} \end{gathered}`

The dimensions of the triangle are

`\begin{gathered} \text{Hyp}=\sqrt[]{10}mi \\ \text{Opp}=xmi \\ \text{Adj}=3mi \end{gathered}`

Substituting the values into the Pythagorean theorem formula above,

`\begin{gathered} (\sqrt[]{10})^2=x^2+3^2 \\ 10=x^2+9^{} \\ \text{Collect like terms} \\ x^2=10-9 \\ x^2=1 \\ \text{Square root of both sides} \\ \sqrt[]{x^2}=\sqrt[]{1} \\ x=1 \end{gathered}`

The missing side, x is 1mi

Answer is D