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ACT Math 1.1 Trigonometry 355 Views


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ACT Math: Trigonometry Drill 1, Problem 1. What is the length of y?

Language:
English Language

Transcript

00:02

Here's your shmoop du jour...

00:04

If sin (A) = 3/5 and x = 10, what is the length of y?

00:11

And here are the potential answers...

00:14

According to SOHCAHTOA, sin is opposite over hypotenuse.

00:20

If sin of angle A is 3 over 5, then the ratio of sides x and z is 3 to 5.

00:26

Since we're told that x equals 10, we can set up a ratio that looks like this. And we

00:31

cross multiply to solve for z.

00:34

We get 10 times 5 equals 50...and 3 times z as 3z. So now divide both sides

00:39

by 3 and we get that z equals around 16.7. And now that we have two side lengths of a

00:45

right triangle, we can use the Pythagorean Theorem to solve for y.

00:49

So now we can just plug in our values.

00:53

10 squared plus y squared equals 16.7 squared. 100 plus y squared equals 278.89. Subtract

01:03

100 from both sides, and we get that y squared equals 178.89.

01:07

Take the square root of both sides, and we get that y equals plus or minus 13.3.

01:14

Sides can't be negative...

01:16

...so the answer is 13.3. So it's A.

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