from a boat, the angle of elevation of the foot of a lighthouse on the edge of a cliff is 34 degrees. if the cliff is 150m high, how far from the base of the cliff is the boat
222m
150/x = tan 34°
C2/sin(a)= I
h= I*cos(a)= 222m
Oh, I've got a good one for you! Why did the boat go to the comedy club? Because it wanted to see some high-flying lighthouse entertainment! Now, let's get down to business. To figure out how far from the base of the cliff the boat is, we'll need a little trigonometry! Since we know the angle of elevation is 34 degrees and the height of the cliff is 150m, we can use the tangent function to solve for the distance. So, the distance from the base of the cliff to the boat is approximately 150m divided by the tangent of 34 degrees. That'll give you your answer!
To solve this problem, we can use trigonometry. Let's break down the information given:
Angle of elevation of the foot of the lighthouse: 34 degrees.
Height of the cliff: 150 meters.
Now, we need to find the distance between the boat and the base of the cliff.
We can visualize a right triangle formed by the boat, the base of the cliff, and the top of the lighthouse. The angle of elevation is the angle between the line of sight from the boat to the foot of the lighthouse and the horizontal line passing through the top of the cliff.
Since we have the angle of elevation and the height of the cliff, we can use the tangent function. 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 cliff, and the adjacent side is the distance between the boat and the base of the cliff. Let's call this distance "x."
Using the tangent function:
tan(34 degrees) = 150 meters / x
Now we can solve for "x."
By rearranging the equation, we get:
x = 150 meters / tan(34 degrees)
Using a scientific calculator or trigonometric table, we can find the tangent of 34 degrees, which is approximately 0.67.
Therefore, we have:
x = 150 meters / 0.67
Evaluating the expression gives us:
x ≈ 224.63 meters
So, the boat is approximately 224.63 meters away from the base of the cliff.