Question Video: Using Right Triangle Trigonometry to Find an Unknown Angle

In the given figure, find the measure of angle πœƒ, in degrees, to two decimal places.

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Video Transcript

In the given figure, find the measure of angle πœƒ in degrees to two decimal places.

In order to solve this problem, we’re going to have to use the sine, cosine, and tangent trigonometrical ratios. sin πœƒ is equal to the opposite divided by the hypotenuse, cos πœƒ is equal to the adjacent divided by the hypotenuse, and tan πœƒ is equal to the opposite divided by the adjacent.

In order to decide which ratio to use, we need to label the sides of our triangle. The longest side β€” the one opposite the right angle β€” is the hypotenuse. The side labelled five is the opposite as it is opposite the angle πœƒ. And the third side is called the adjacent as it is next to or adjacent to the angle πœƒ. As the opposite is equal to five and the hypotenuse is equal to 11, we will use the sine ratio. sin πœƒ is equal to five divided by 11.

In order to calculate the angle πœƒ, we need to use the inverse sine operation. Therefore, πœƒ is equal to inverse sine of five 11ths. Typing this into our calculator gives us an answer of πœƒ equals 27.04 degrees to two decimal places. Therefore, the measure of the angle πœƒ is 27.04.

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