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ACT Math 5.4 Trigonometry 246 Views


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Description:

ACT Math: Trigonometry Drill 5, Problem 4. What is the measure of the angle?

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English Language

Transcript

00:02

Here's your shmoop du jour

00:05

If tan(x) = square root of 3, what is the measure of the angle?

00:09

And here are the potential answers...

00:14

It's asking us to find x, or the measure of the angle that makes the tangent of x equal

00:19

to root 3.

00:21

Remember your triangle trig ratios?

00:22

Tangent is opposite over adjacent.

00:27

The ratio of the opposite side of the angle x over the adjacent side to x is the square root of

00:33

3 or root 3 over 1. Okay. Pythagorean Theorem time!

00:37

squared.

00:37

One squared plus root three squared equals the hypotenuse squared. One plus three equals

00:44

the hypotenuse squared... so four equals the hypotenuse squared.

00:48

Take the square root of both sides, and we get that the hypotenuse equals 2.

00:53

The ratio of the sides is 1 to √3 to 2, which means this is a special triangle.

01:03

It's a 30-60-90 triangle, and x, the angle opposite the second longest side is the second

01:08

largest angle, which makes it 60 degrees. Option D is the correct answer.

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