Reed is snorkeling when he spots a stingray resting on the bottom of the ocean floor. He is on the surface of the water looking down. The water is 22 feet deep and the diagonal distance from him to the fish is 34 feet. Use the inverse of cosine to find the approximate angle of elevation with which he is looking at the fish.(1 point) Responses 65° 65° 50° 50° 40° 40° 90°
To find the angle of elevation, we can use the inverse cosine function, also known as the arccosine function.
The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is the depth of the water, which is 22 feet, and the hypotenuse is the diagonal distance from Reed to the stingray, which is 34 feet.
So, we can write the equation as: cos(angle) = 22/34
To find the angle, we take the inverse cosine (arccosine) of both sides: angle = arccos(22/34)
Using a calculator, we can find that arccos(22/34) is approximately equal to 50.1 degrees.
Therefore, the approximate angle of elevation with which Reed is looking at the fish is 50°.