How to find an angle with sine

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ACT Math › How to find an angle with sine

Questions 1 - 4
1

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.

Explanation

You can draw your scenario using the following right triangle:

Theta1

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

or .

2

Theta2

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

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 .

3

For the triangle Using_sin_to_find_angle, find in degrees to the nearest integer

Note: The triangle is not necessarily to scale

None of the other answers

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

4

Simplify: (sinΘ + cosΘ)2

2sinΘcosΘ -1

1 + cos2Θ

cos2Θ -1

1 + sin2Θ

None of the answers are correct

Explanation

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

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