The side of a lake has a uniform angle of elevation of 15 degrees 30 feet. How far up the side of the lake does the water rise if the height of the lake increases by 7.3 feet during flood season.

To determine how far up the side of the lake the water rises, we need to use trigonometry.

First, let's label the given information:
Angle of elevation: 15 degrees
Height increase: 7.3 feet

Using trigonometry, we can apply the tangent function to find the distance. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the height increase of 7.3 feet is the opposite side, and the distance we are trying to find is the adjacent side. We can set up the equation as follows:
tan(15 degrees) = (opposite side) / (adjacent side)

Now, let's solve for the adjacent side:
(adjacent side) = (opposite side) / tan(15 degrees)

Substituting the given values:
(adjacent side) = 7.3 / tan(15 degrees)

To find the value of tan(15 degrees), we can use a scientific calculator or an online calculator.

By inputting "tan(15 degrees)" into a calculator, we get approximately 0.2679.

Let's substitute this value into the equation:
(adjacent side) = 7.3 / 0.2679

Now, dividing 7.3 by 0.2679 gives us approximately 27.2.

Therefore, the water rises approximately 27.2 feet up the side of the lake during flood season.

wouldn't it be 7.3/sinTheta ?