When the sun is 30degree above the horizon.calculate the length of the shadow cast by a towdr 24 high. with the diagram
If the length of the shadow is x units
then tan 30° = 24/x
x = 24/tan30° = ...
or
x = 24cot30° = ..... , same thing
To calculate the length of the shadow cast by a tower, we can use basic trigonometry. In this case, we will use the tangent function.
Here's how you can calculate the length of the shadow:
Step 1: Draw a diagram:
- Draw a vertical line to represent the tower and label it as the tower's height (24 units).
- Draw a horizontal line starting from the bottom of the tower to represent the length of the shadow.
- Angle θ between the ground and the line from the top of the tower to the sun is given as 30 degrees.
Step 2: Identify the trigonometric relationship:
- In this case, we need to use the tangent function: tan(θ) = opposite / adjacent.
Step 3: Identify the opposite and adjacent sides:
- The height of the tower is the opposite side.
- The length of the shadow is the adjacent side.
Step 4: Set up the equation using the tangent function:
- tan(θ) = opposite / adjacent
- tan(30°) = 24 / x (where x is the length of the shadow)
Step 5: Solve for x:
- Multiply both sides of the equation by x: x * tan(30°) = 24
- Divide both sides of the equation by tan(30°): x = 24 / tan(30°).
Step 6: Calculating the length of the shadow:
- Use a scientific calculator to find the tangent of 30 degrees: tan(30°) ≈ 0.577.
- Substitute the value into the equation: x = 24 / 0.577 ≈ 41.57 units.
Therefore, the length of the shadow cast by the tower when the sun is 30 degrees above the horizon is approximately 41.57 units.