Question

question 13 of 25
the side lengths of a 45 - 45 - 90 triangle are in the ratio ( 1:1:sqrt{2} ). what is ( sin 45^{circ} )?
a. ( \frac{sqrt{2}}{2} )
b. ( \frac{1}{2} )
c. 1
d. ( sqrt{2} )

Explanation:

Step1: Recall sine definition

$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Assign sides to 45-45-90 triangle

Let legs = 1, hypotenuse = $\sqrt{2}$

Step3: Calculate $\sin45^\circ$

$\sin45^\circ = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$

Answer:

A. $\frac{\sqrt{2}}{2}$