Question

18. What is the value of x in the right triangle? 9 х A) 7 B) 777 C) 785 D) V7

Answer 1

Given a right-angled triangle

Where

`\begin{gathered} \text{Hyp}=\text{Hypotenuse}=9\text{ units} \\ \text{Adj}=\text{Adjacent}=2\text{ units} \\ \text{Opp}=\text{Opposite}=x\text{ units} \end{gathered}`

The value of x can be deduced by using the Pythagorean theorem

The formula of the Pythagorean theorem is

`\text{Hyp}^2=\text{Opp}^2+\text{Adj}^2`
`9^2=x^2+2^2`

Solve for x

`\begin{gathered} 9^2=x^2+2^2 \\ 81=x^2+4 \\ \text{Collect like terms} \\ x^2=81-4 \\ x^2=77 \\ \text{Square of both sides} \\ \sqrt[]{x^2}=\sqrt[]{77}^{} \\ x=\sqrt[]{77}\text{ units} \end{gathered}`

Hence, the answer is option B