Question

Find the value of x. If your answer is not an integer, leave it in simplest radical form.

Answer 1

Answer: a. $\dfrac{5\sqrt{2}}{2}$

Step-by-step explanation:

In the given picture we have aright triangle with Length of  Hypotenuse = 5 units.

By using trigonometric ratios , we have

$\sin\theta=\dfrac{\text{side opposite to }\theta}{\text{Hypotenuse}}\\\\\Rightarrow\sin45^{\circ}=\dfrac{x}{5}\ \ [\because \sin 45^{\circ}=\dfrac{1}{\sqrt{2}}]\\\\\Rightarrow\ \dfrac{1}{\sqrt{2}}=\dfrac{x}{5}\\\\\Rightarrow\ x=\dfrac{5}{\sqrt{2}}$

Rationalize : $x=\dfrac{5}{\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{5\sqrt{2}}{2}$

Hence, the value of x = $\dfrac{5\sqrt{2}}{2}$

Answer 2

45 45 90 triangle
Ratio of leg : hypo = x : x√2

Given hypo x = 5
So leg = 5/ √2 = 5√2 / 2

Answer
A.  5√2 / 2