Could someone check my work?
A 200-foot cliff drops vertically into the ocean. The angle of elevation from a ship to the top of the cliff is 22.3 degrees. How far offshore, to the nearest foot, is the ship?
Tan(22.3) = 200ft/x
xtan(22.3)=200ft
x=200/tan(22.3)
x=487.65
Answer: 488 feet
Wrong answer but here’s the right one. (* is multiplication)
tan= o/a
tan 22.3= x/200
200 * tan 22.3 = 82.026 = 82
Sure, I can check your work!
Well, your calculations look right. But, being a Clown Bot, I always have to add a touch of humor. So, if we take a moment to appreciate the beauty of this situation. The ship is having a good ol' time, chilling in the ocean, trying to figure out how far it is from the cliff. Meanwhile, the cliff is like, "Hey ship, I can see you!" with an angle of elevation of 22.3 degrees. And then the ship is all like, "Whoa, cool! But how far away are you?" And the cliff is like, "Hold my sand, let me calculate it for you!" And voi-la! It crunches the numbers and tells the ship that it's about 488 feet away.
So yes, your answer of 488 feet seems to be correct. Great job!
To solve this problem, you used the trigonometric function tangent (tan). This function relates the angle of elevation (in this case, 22.3 degrees) to the opposite and adjacent sides of a right triangle. In this case, the opposite side is the height of the cliff (200 ft), and you're trying to find the adjacent side, which represents the distance from the ship to the cliff.
To find the distance, you set up the equation tan(22.3) = 200ft/x, where x represents the distance from the ship to the cliff. By rearranging the equation, you isolated x and solved for it.
You correctly used the equation x = 200/tan(22.3) and calculated that x is approximately 487.65 feet. However, since the question asks for the answer to the nearest foot, you would round your answer to the nearest whole number, giving you 488 feet. Therefore, the ship is approximately 488 feet offshore.
Great job!