The angle of depression from the top of a lighthouse to a boat in the water is 30°. If the lighthouse is 89 feet tall how far is the boat from the lighthouse to the nearest foot?
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10Take this time to do your
best on this question.
A)
45 feet Eliminate Reactivate
B)
51 feet Eliminate Reactivate
C)
63 feet Eliminate Reactivate
D)
154 feet Eliminate Reactivate
tan 30° = 89/x
x = 89/tan30°
= ...
I have no idea what the rest of your post means, or how it ties in with your question.
D does contain the number 154 ft, which is the correct answer.
To find the distance from the boat to the lighthouse, we can use trigonometry. In this case, we can use the tangent function.
According to the problem, the angle of depression from the top of the lighthouse to the boat is 30°. The tangent of an angle is equal to the opposite side divided by the adjacent side.
Let's assume the distance from the boat to the base of the lighthouse is "x" feet. We can form a right triangle with the height of the lighthouse (89 feet) being the opposite side and the distance "x" being the adjacent side.
Therefore, we can set up the following equation:
tan(30°) = 89 / x
To find the value of x, we can multiply both sides of the equation by x:
x * tan(30°) = 89
Now, we need to solve for x. We can use a scientific calculator to find the tangent of 30°, which is approximately 0.5774.
x * 0.5774 = 89
Dividing both sides of the equation by 0.5774, we get:
x ≈ 89 / 0.5774 ≈ 154
Therefore, the distance from the boat to the lighthouse is approximately 154 feet.
So, the answer is D) 154 feet.
To solve this problem, we can use trigonometry. The angle of depression is the angle formed between a horizontal line and a line of sight from the top of the lighthouse to the boat. In this case, the angle of depression is given as 30°.
We can use the tangent function to find the distance from the lighthouse to the boat. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the lighthouse (89 feet), and we want to find the adjacent side, which is the distance from the lighthouse to the boat.
Let's call the distance from the lighthouse to the boat "x". Now we can set up the equation:
tan(30°) = 89 / x
To solve for x, we can rearrange the equation:
x = 89 / tan(30°)
To calculate this, we can use a scientific calculator or refer to a trigonometric table. In this case, the value of tan(30°) is approximately 0.577.
Now we can substitute this value into the equation:
x = 89 / 0.577 ≈ 154
Therefore, the distance from the lighthouse to the boat is approximately 154 feet.
So the correct answer is option D) 154 feet.