In the given figure, find the measure of angle 𝜃 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 𝜃 is equal to the opposite divided by the hypotenuse, cos 𝜃 is equal to the adjacent divided by the hypotenuse, and tan 𝜃 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 — the one opposite the right angle — is the hypotenuse. The side labelled five is the opposite as it is opposite the angle 𝜃. And the third side is called the adjacent as it is next to or adjacent to the angle 𝜃. As the opposite is equal to five and the hypotenuse is equal to 11, we will use the sine ratio. sin 𝜃 is equal to five divided by 11.
In order to calculate the angle 𝜃, we need to use the inverse sine operation. Therefore, 𝜃 is equal to inverse sine of five 11ths. Typing this into our calculator gives us an answer of 𝜃 equals 27.04 degrees to two decimal places. Therefore, the measure of the angle 𝜃 is 27.04.