Lee is on a cliff 360 m above sea level, the angle of depression of a ship is 28 degrees. To the nearest meter, what is the distance between the ship and the base of the cliff?
tan28=x/360?
Nope. cot28 = x/360
Yes, you are correct. We can use the tangent function to solve this problem. Let's set up the equation using the information given:
tan(28°) = x/360
To solve for x, we'll multiply both sides of the equation by 360:
360 * tan(28°) = x
Using a calculator, we find that tan(28°) ≈ 0.5317. Now we can substitute this value into the equation:
360 * 0.5317 ≈ 190.812
Therefore, the distance between the ship and the base of the cliff is approximately 191 meters when rounded to the nearest meter.
Yes, you're on the right track! To find the distance between the ship and the base of the cliff, you can use trigonometry and specifically the tangent function.
Let's represent the distance between the ship and the base of the cliff as 'x'. We have the angle of depression, which is the angle formed between the line of sight from Lee to the base of the cliff and the horizontal line formed by the sea level.
Now, we can use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle. In this case, the opposite side is the height of the cliff (360 m) and the adjacent side is the distance 'x' between the ship and the base of the cliff.
So, the equation becomes tan(28°) = 360/x.
Now, we can solve for 'x' by rearranging the equation:
x = 360/tan(28°).
Calculating that on a calculator, we get:
x ≈ 630.20 m.
Therefore, to the nearest meter, the distance between the ship and the base of the cliff is approximately 630 meters.