A 2 m tall person standing on the ground looks up at an angle of 34.0 o with the horizontal and sees the top of a tree and the top of a building aligned. The tree is 20 m away from the person, and the building is 51.0 m from the person
To find the height of the tree and the building, we can use trigonometry and create a right triangle with the person's eye level as one side, the distance to the tree/building as another side, and the height of the tree/building as the hypotenuse.
First, let's calculate the height of the tree:
1. Begin by finding the vertical distance from the person's eye level to the top of the tree. We can use the tangent function to do this.
tan(angle) = opposite / adjacent
tan(34.0 degrees) = height of tree / distance to tree
height of tree = tan(34.0 degrees) × 20 m
2. Calculate the actual height of the tree by adding the height of the person to the height from the previous step.
actual height of tree = height of person + height of tree
Next, let's calculate the height of the building:
1. Use the same method as above to find the vertical distance from the person's eye level to the top of the building.
tan(angle) = opposite / adjacent
tan(34.0 degrees) = height of building / distance to building
height of building = tan(34.0 degrees) × 51.0 m
2. Calculate the actual height of the building by adding the height of the person to the height from the previous step.
actual height of building = height of person + height of building
By following these calculations, you can determine the actual height of both the tree and the building.