# ACT Math : How to find an angle with sine

## Example Questions

### Example Question #1 : How To Find An Angle With Sine

Simplify: (sinΘ + cosΘ)2

Possible Answers:

cos2Θ -1

None of the answers are correct

1 + sin2Θ

1 + cos2Θ

2sinΘcosΘ -1

Correct answer:

1 + sin2Θ

Explanation:

Using the foil method, multiply.  Simplify using the Pythagorean identity sin2Θ + cos2Θ = 1 and the double angle identity sin2Θ = 2sinΘcosΘ.

### Example Question #2 : How To Find An Angle With Sine

For the triangle , find  in degrees to the nearest integer

Note: The triangle is not necessarily to scale

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To solve this equation, it is best to remember the mnemonic SOHCAHTOA which translates to Sin = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Looking at the problem statement, we are given the side opposite of the angle we are trying to find as well as the hypotenuse. Therefore, we will be using the SOH part of our mnemonic. Inserting our values, this becomes . Then, we can write . Solving this, we get

### Example Question #3 : How To Find An Angle With Sine

A fifteen foot ladder is leaned up against a twelve foot building, reaching the top of the building. What is the angle made between the ladder and the ground? Round to the nearest hundredth of a degree.

Possible Answers:

Correct answer:

Explanation:

You can draw your scenario using the following right triangle:

Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:

or .

### Example Question #4 : How To Find An Angle With Sine

What is the value of  in the right triangle above? Round to the nearest hundredth of a degree.

Possible Answers:

Correct answer:

Explanation:

Recall that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse of the triangle. You can solve for the angle by using an inverse sine function:

or .

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