A tree casts a shadow that measures 4 ft, At the same time, a yardstick casts a shadow that is 9 in long. How tall is the pole?
Assuming that the light comes from the same sources (in this case, the sun), the ratio of the yardstick (one yard) and its shadow (9 inches) equal the ratio of the height of the tree(pole) over 4 feet. Using that equation, convert all measures to the same units and solve.
I hope this helps. Thanks for asking.
To solve this problem, we need to set up a proportion between the yardstick and its shadow, and the height of the pole and its shadow.
Let's first convert the measurements to the same unit. Since the yardstick's shadow is given in inches, let's convert the height of the pole's shadow to inches as well.
We know that 1 yard equals 36 inches. So, the yardstick's shadow of 9 inches is equivalent to (9/36) yards.
Now, let's set up the proportion:
(height of pole) / (shadow of pole) = 1 yard / (shadow of yardstick)
Let's substitute the values we know:
(height of pole) / 4 ft = 1 yard / (9/36) yards
Simplify the equation by converting the feet to yards:
(height of pole) / 4 = 1 / (9/36)
To simplify the equation further, multiply both sides of the equation by 4:
4 * (height of pole) / 4 = (1 / (9/36)) * 4
Simplify the right side:
(height of pole) = (1 / (9/36)) * 4
Now, perform the calculations:
(height of pole) = 1 * (36/9) * 4
(height of pole) = 4 * 4
(height of pole) = 16
Therefore, the height of the pole is 16 feet.
I hope this explanation was helpful! Let me know if you have any further questions.