A geologist at point A measures the distance and angle of elevation to two columns of the Glen Rose formation in Texas. If the distance AS=796 ft and the distance AN=850 ft, compute the difference in the heights of the two columns to the nearest foot.
What do I need to do to solve this problem?
To solve this problem, you need to use trigonometry and the given distances and angles of elevation. Specifically, you will use the tangent function.
Here are the steps to solve the problem:
1. Draw a diagram: Draw a right triangle to represent the scenario, with point A at the right angle. Label the sides and angles of the triangle based on the given information.
2. Identify the sides and angle: In the diagram, the side opposite angle A is AN, and the side adjacent to angle A is AS. The height difference between the two columns of the Glen Rose formation is represented by the side opposite angle S.
3. Use the tangent function: The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, we can use the tangent function to relate the angle S and the height difference.
tan(S) = height difference / AS
4. Solve for the height difference: Rearrange the tangent equation to solve for the height difference:
height difference = tan(S) * AS
5. Substitute the given values and calculate: Plug in the values for angle S (given as angles of elevation) and AS:
height difference = tan(S) * AS
Since the given angle of elevation is not provided in the question, we are unable to determine the height difference based on the given information.