Answer:
As per the statement:
The angle of depression of a boat at sea from a 100 foot lighthouse is 20 degrees.
We draw the figure for this problem as shown below:
Height of the lighthouse(BC) = 100 foot
Angle of depression = 20 degrees.
Since, angle of depression is equal to the angles of elevation
i.e,
using tangent ratio:
Here,
Opposite side = BC = 100 foot
Adjacent side = AB
Angle of elevation:
Substitute these to solve for AB:
or
Simplify:
AB = 294.375362123 foot
Therefore, the distance to the boat approximately is 294.4 foot
By using the tangent function with the given height of the lighthouse and the angle of depression, we can solve for the distance to the boat, which is approximately 274.1 feet.
In this scenario, we can use trigonometry to find the distance to the boat. Since we know that the lighthouse is 100 feet high and the angle of depression is 20 degrees, this fits the scenario for a tangent function, where tangent of an angle equals the opposite side divided by the adjacent side.
Setting up our function, we get tan(20) = 100/ distance to the boat. Since we want to find the distance to the boat, we can rearrange the equation to be distance to the boat = 100 / tan(20).
Doing this calculation, we find that the distance to the boat is approximately 274.1 feet.
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Mary's average speed for the round trip was 2.4 miles per hour, calculated by dividing the total distance of the trip (6 miles) by the total time for the trip (2.5 hours).
The question deals with calculating average speed for a round trip. The total distance for Mary's walk was 6 miles (3 miles to the park and 3 miles back). The total time taken for the walk was 2.5 hours (1 hour to get to the park and 1.5 hours to return).
Average speed is calculated by dividing total distance by total time. So, the average speed of Mary's round trip is 6 miles divided by 2.5 hours, which equates to 2.4 miles per hour.
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