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 will need to find the angles of elevation of the two columns.
To solve this problem, you need to use trigonometry, specifically the tangent function, to find the heights of each column.
Here are the steps to follow:
1. Draw a diagram: Draw a right triangle to represent the situation. Label point A as the geologist's location, and draw lines to represent the two columns (S and N). Label the distance from point A to column S as AS and distance from point A to column N as AN.
2. Identify the angle of elevation: The angle of elevation is the angle between the horizontal line passing through point A and the line of sight to the columns. This angle is not provided in the question, so you may need to observe or assume a value based on context. Let's assume the angle of elevation to column S is θ1 and to column N is θ2.
3. Use the tangent function: The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the columns and the adjacent side is the horizontal distance from point A.
So, for column S:
tan(θ1) = height of S / AS
And for column N:
tan(θ2) = height of N / AN
4. Solve for the heights: Rearrange the above equations to solve for the heights of each column. Multiply both sides of the equations by the adjacent sides to isolate the heights:
height of S = AS * tan(θ1)
height of N = AN * tan(θ2)
5. Find the difference in heights: Subtract the height of column N from the height of column S to get the difference in heights:
Difference in heights = height of S - height of N
(round this value to the nearest foot)
By following these steps and plugging in the actual values for AS, AN, and the respective angles of elevation, you can find the difference in heights of the two columns of the Glen Rose formation in Texas.