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ACT Math: Trigonometry Drill 1, Problem 1. What is the length of y?
ACT Math: Coordinate Geometry Drill 1, Problem 2. Solve the inequality and determine which solution is shown on the number line.
ACT Math 1.1 Trigonometry 355 Views
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ACT Math: Trigonometry Drill 1, Problem 1. What is the length of y?
- Trigonometry / Solving right triangles
- Trigonometry / SOHCAHTOA (values and properties of trig functions)
- Product Type / ACT Math
- Foreign Language / Arabic Subtitled
- Foreign Language / Spanish Subtitled
- Foreign Language / Korean Subtitled
- Foreign Language / Chinese Subtitled
- Trigonometry / Trigonometric relations in right triangles
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.
Full Transcript
- 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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