From the top of a lighthouse 210 feet high, the angle if depression to a boat is 27 degress. Find the distance from the boat to the food of the lighthouse. The lighthouse was built at sea level.

Check 4-18-11,1:42pm post for solution.

To find the distance from the boat to the foot of the lighthouse, we can use trigonometry.

Let's label the distance we want to find as "x". We can create a right-angled triangle with one side representing the height of the lighthouse (210 ft) and another side representing the distance from the boat to the foot of the lighthouse (x ft).

The angle of depression is the angle between the line of sight from the top of the lighthouse to the boat and the horizontal line formed by the base of the lighthouse. In this case, the angle of depression is 27 degrees.

Since we have a right-angled triangle and we know one angle, we can use the trigonometric function tangent (tan) to relate the angle and the sides of the triangle:

tan(angle) = opposite/adjacent

In this case, the angle is the angle of depression (27 degrees), the opposite side is the height of the lighthouse (210 ft), and the adjacent side is the distance we want to find (x ft):

tan(27 degrees) = 210 ft / x ft

To find x, we can rearrange the equation:

x ft = 210 ft / tan(27 degrees)

Now, we can calculate the distance using a calculator or by plugging the values into a trigonometric calculator.

x ≈ 436.10 ft

Therefore, the distance from the boat to the foot of the lighthouse is approximately 436.10 feet.