Question

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

Answer 1

Answer:

$\frac{5\sqrt{2} }{2}$

Step-by-step explanation:

$x: \text{opposite side of the angle of 45\º}$

$5: \text{hypotenuse of the right triangle}$

$\sin(\theta)=\frac{\text{opp}}{\text{hyp}} \Rightarrow \sin(45\º)=\frac{x}{5}$

$\text{Once }\sin(45\º)=\frac{\sqrt{2} }{2}$

$\frac{\sqrt{2} }{2} =\frac{x}{5} \Rightarrow 2x=5\sqrt{2} \Rightarrow x=\frac{5\sqrt{2} }{2}$

You can just remember that 5 is the diagonal of a square of side length x.

$5=x\sqrt{2} \Rightarrow x=\frac{5}{\sqrt{2} } \Rightarrow x=\frac{5}{\sqrt{2} } \cdot \frac{\sqrt{2} }{\sqrt{2} } = \frac{5\sqrt{2} }{2}$