Question

A 30° 60° 90° triangle is shown below. Find the length of the side labeled y.

Answer 1

Answer:

Part 1) $y=3\ units$

Part 2) The length of the hypotenuse is 6 units

Step-by-step explanation:

Part 1) we know that

In the right triangle of the figure

$sin(60^o)=\frac{y}{2\sqrt{3}}$ ----> by SOH (opposite side divided by the hypotenuse)

solve for y

$y=sin(60^o)2\sqrt{3}$

Remember that

$sin(60^o)=\frac{\sqrt{3}}{2}$

substitute

$y=(\frac{\sqrt{3}}{2})2\sqrt{3}$

$y=3\ units$

Part 2)

Let

h ----> the length of the hypotenuse

we know that

In the right triangle of the figure

$sin(45^o)=\frac{3\sqrt{2}}{h}$ ----> by SOH (opposite side divided by the hypotenuse)

$h=\frac{3\sqrt{2}}{sin(45^o)}$

Remember that

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

substitute

$h=3\sqrt{2}:\frac{\sqrt{2}}{2}$

$h=6\ units$