Question

How do I find the value of x with a given of two sides and one angle i need to find the missing side

Answer 1

To find a missing side in a right rtaingle as given use Pythagorean theorem:

`hypotenuse^2=Leg1^2+Leg2^2`

Misising side in given triangle is a Leg:

`\begin{gathered} Subtract\text{ Leg2}^2\text{ from both sides of the equation:} \\ hypotenuse^2-Leg2^2=Leg1^2+Leg2^2-Leg2^2 \\ hypotenuse^2-Leg2^2=Leg1^2 \\ \\ Rewrite_ \\ Leg1^2=hypotenuse^2-Leg2^2 \\ Take\text{ square root of both sides of the equation:} \\ √(Leg1^2)=√(hypotenuse^2-Leg2^2) \\ Leg1=√(hypotenuse^2-Leg2^2) \end{gathered}`

`Leg1=√(hypotenuse^2-Leg2^2)`
`\begin{gathered} x=√(21^2-10^2) \\ x=√(441-100) \\ x=√(341) \\ x\approx18.47 \end{gathered}`Then, the approximate value of x is 18.47Answer: A