How tall is a man that casts a shadow at the same time a 40 ft. building casts a 60 ft shadow?
How long is the man's shadow?
To determine the height of the man, we can use the concept of similar triangles. Similar triangles have corresponding angles that are equal and proportional sides.
In this case, we have a right triangle formed by the man's height, the length of his shadow, and the length of the building's shadow. Let's assume the height of the man is represented by 'x'.
Using the concept of similar triangles, we can set up the following proportion:
(man's height)/(length of man's shadow) = (building's height)/(length of building's shadow)
x/40 = 40/60
Now, let's solve this proportion to find the value of 'x':
Cross-multiplying, we get:
60x = 40 * 40
Dividing both sides by 60:
x = (40 * 40) / 60
Simplifying, we find:
x = 1600 / 60 = 26.67 ft
Therefore, the man's height is approximately 26.67 feet.