The Leaning tower of pisa is 55.9m tall and leans 5.5 degrees from the vertical. If its shadow is 90.0m long, what is the distance from the top of the tower to the top of the edge of it’s shadow? Assume that the ground is level.
You don't say if the sun is showing on its forward or its backwards leaning side.
One triangle would have sides of 55.9m 90 m and an angle of 84.5° between
simple application of the cosine law to find the distance between the end of the shadow and the top of the tower.
Repeat the calculation using an angle of 95.5° for the other case
No, it’s not right instead of subtracting 5.5 degree from 90, you should add 5.5 into 90. Then you will get the right answer.
To find the distance from the top of the tower to the top of the edge of its shadow, we can use trigonometry. Here are the steps:
Step 1: Identify the right triangle formed by the height of the tower, the distance from the top of the tower to the top of the edge of its shadow, and the length of the shadow.
Step 2: Calculate the length of the adjacent side of the right triangle, which is the horizontal distance from the top of the tower to the top of the edge of its shadow. We can use the formula: adjacent = shadow * tan(angle).
In this case, the shadow length is 90.0m and the angle is 5.5 degrees.
adjacent = 90.0m * tan(5.5 degrees)
Step 3: Calculate the hypotenuse of the right triangle, which is the distance from the top of the tower to the top of the edge of its shadow. We can use the formula: hypotenuse = height / cos(angle).
In this case, the height of the tower is 55.9m and the angle is 5.5 degrees.
hypotenuse = 55.9m / cos(5.5 degrees)
Step 4: Calculate the opposite side of the right triangle, which is the vertical distance from the top of the tower to the top of the edge of its shadow. We can use the formula: opposite = hypotenuse * sin(angle).
In this case, the hypotenuse is the distance we calculated in Step 3, and the angle is 5.5 degrees.
opposite = hypotenuse * sin(5.5 degrees)
The result will give us the distance from the top of the tower to the top of the edge of its shadow.
To find the distance from the top of the tower to the top of the edge of its shadow, we can use trigonometry. Let's break down the problem step by step:
1. Draw a diagram: Start by visualizing the scenario described in the question. Draw a vertical line to represent the tower, and draw a line from the top of the tower to the edge of its shadow.
2. Label the given information: On the diagram, label the height of the tower as 55.9m and the angle of lean as 5.5 degrees.
3. Identify the relevant trigonometric function: Since we want to find the length of the line connecting the top of the tower to the edge of its shadow, we will use the tangent function. Recall that tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle.
4. Set up the equation: We can use the tangent function to set up the equation. The opposite side in this case is the height of the tower (55.9m), and the adjacent side is the distance from the top of the tower to the edge of its shadow (which we need to find).
Tangent(angle) = opposite/adjacent
tan(5.5 degrees) = 55.9m/adjacent
5. Solve for the unknown: Rearrange the equation to solve for the adjacent side (distance from the top of the tower to the edge of its shadow).
adjacent = 55.9m / tan(5.5 degrees)
6. Calculate the value: Use a calculator or a mathematical software to evaluate the tangent of 5.5 degrees and divide 55.9m by the result.
adjacent ≈ 571.17m
Therefore, the distance from the top of the tower to the top of the edge of its shadow is approximately 571.17 meters.