A tree casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. What is the height of the tree?
Correct Answer: 10 meters
- Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the tree to the sun.
- Step 2: Know that when the angle of elevation is 45 degrees, the height of the tree and the length of the shadow are equal.
- Step 3: Use the formula for height, which is height = shadow * tan(angle).
- Step 4: Since the angle is 45 degrees, tan(45) equals 1.
- Step 5: Substitute the values into the formula: height = 10 meters (shadow) * 1 (tan(45)).
- Step 6: Calculate the height: height = 10 * 1 = 10 meters.
- Trigonometry – The relationship between angles and sides in right triangles, specifically using the tangent function.
- Angle of Elevation – The angle formed by the horizontal line and the line of sight to an object above the horizontal.
- Shadow Length – The distance from the base of an object to the tip of its shadow, which can be used to determine height using trigonometric ratios.
