The height of a ski slope is 16 meters and its length is 20 meters. Find the measure of angle 𝜃, giving the answer to two decimal places.
In order to answer this question, we will use our knowledge of the trigonometric ratios in right triangles. We know that the sin of angle 𝜃 is equal to the opposite over the hypotenuse. The cos of 𝜃 is the adjacent over the hypotenuse. And the tan of 𝜃 is equal to the opposite over the adjacent. One way of remembering these ratios is using the acronym SOH CAH TOA. We know that the longest side of our triangle, which is opposite the right angle, is the hypotenuse. The side that is opposite the angle we are dealing with, in this case 𝜃, is known as the opposite. And finally, the side that is next to the angle we are dealing with and the right angle is known as the adjacent.
In this question, we know that the length of the opposite side is 60 meters. This is the height of the ski slope. And as the length of the ski slope is 20 meters, the hypotenuse is 20 meters. We will therefore use the sine ratio. And substituting in our values, we have sin 𝜃 is equal to 16 over 20. Both the numerator and denominator of our fraction are divisible by four. Therefore, sin 𝜃 is also equal to four-fifths. We can then take the inverse sine of both sides of our equation such that 𝜃 is equal to the inverse sin of four-fifths. Typing this into our calculator whilst ensuring we’re in degree mode gives us 𝜃 is equal to 53.1301 and so on degrees. We are asked to give our answer to two decimal places. The measure of angle 𝜃 to two decimal places is 53.13 degrees.