Question Video: Using Right Triangle Trigonometry to Find an Unknown Angle Mathematics • 11th Grade

In the given figure, find the measure of angle ๐œƒ, in degrees, to two decimal places.

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Video Transcript

In the given figure, find the measure of angle ๐œƒ in degrees to two decimal places.

In order to solve this problem, weโ€™re going to have to use the sine, cosine, and tangent trigonometrical ratios. sin ๐œƒ is equal to the opposite divided by the hypotenuse, cos ๐œƒ is equal to the adjacent divided by the hypotenuse, and tan ๐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 โ€” the one opposite the right angle โ€” is the hypotenuse. The side labelled five is the opposite as it is opposite the angle ๐œƒ. And the third side is called the adjacent as it is next to or adjacent to the angle ๐œƒ. As the opposite is equal to five and the hypotenuse is equal to 11, we will use the sine ratio. sin ๐œƒ is equal to five divided by 11.

In order to calculate the angle ๐œƒ, we need to use the inverse sine operation. Therefore, ๐œƒ is equal to inverse sine of five 11ths. Typing this into our calculator gives us an answer of ๐œƒ equals 27.04 degrees to two decimal places. Therefore, the measure of the angle ๐œƒ is 27.04.

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