A 6-foot ladder touches the side of a building at a point 5 feet above the ground. At what height would a 15-foot ladder touch the building if it makes the same angle with the ground as the shorter ladder?
(5 foot height/6 foot ladder)(15 foot ladder) = 75/6 = 12.5 foot height
Katie is 100 cm tall and is standing so that her mother's shado covers her shadow. She is 90 cm from her mother and her mother's shadow is 225cm long. How tall is her mother?
a 12-foot thre cast a 22-foot shaadow. Find the angle of the elevation from the tip of the tree.
To solve this problem, we can use the concept of similar triangles. Let's denote the height that the 15-foot ladder would touch the building as 'x'.
We have two similar right triangles formed by the ladders and the building: one with the 6-foot ladder and the other with the 15-foot ladder. The ratio of the corresponding sides of similar triangles is equal.
In this case, the ratio of the lengths of the ladders will be the same as the ratio of the heights they touch the building. So, we can set up the following proportion:
6 feet / 5 feet = 15 feet / x
To solve for 'x', we can cross-multiply:
6x = 75
Divide both sides of the equation by 6:
x = 75 / 6
Simplifying the fraction:
x = 12.5 feet
Therefore, a 15-foot ladder would touch the building at a height of 12.5 feet.