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lorasvet [3.4K]
3 years ago
12

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

Mathematics
1 answer:
bulgar [2K]3 years ago
7 0

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

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