Question

For the right triangles below, find the exact values of the side lengths b and a If necessary, write your responses in simplified radical form, 음 30° Х 5 ? b 459 2 a a = 0 609 3

Answer 1

a=√2 and b= 3√3

1) Let's find the measure of b, on the triangle on the left.

Let's use for that the tangent of 60º since it relates the opposite and the adjacent leg to angle 60º

`\begin{gathered} \tan \text{ (60) =}(b)/(3) \\ \sqrt[]{3}=(b)/(3) \\ b=3\sqrt[]{3} \end{gathered}`

2) Let's proceed to find side a, on the triangle at the right, this time we'll use the sine of (45º) =

`\begin{gathered} \sin (45)=(a)/(2) \\ \frac{\sqrt[]{2}}{2}=(a)/(2) \\ 2a\text{ =2}\sqrt[]{2} \\ a\text{ =}\sqrt[]{2} \end{gathered}`

3) So the answers are a=√2 and b= 3√3