Question

1. a yardstick held vertically on level ground casts a shadow 16 in. long. what would be the distance from the top of the yardstick to the edge of its shadow?

Explanation:

Step1: Convert yardstick length to inches

A yardstick is 36 inches long.

Step2: Identify right - triangle

The yardstick, its shadow, and the line from the top of the yardstick to the edge of the shadow form a right - triangle. Let the height of the yardstick be $a = 36$ inches and the length of the shadow be $b=16$ inches. We want to find the hypotenuse $c$.

Step3: Apply Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 36$ and $b = 16$ into the formula: $c=\sqrt{36^{2}+16^{2}}=\sqrt{1296 + 256}=\sqrt{1552}$.

Step4: Simplify the square - root

$\sqrt{1552}=\sqrt{16\times97}=4\sqrt{97}\approx4\times9.85=39.4$ inches.

Answer:

$4\sqrt{97}\approx39.4$ inches