Question

the dimensions of a sailboats mainsail are shown below. what is the height of the sail? 32.5 ft 12.5 ft a. 30.7 feet b. 32.5 feet c. 30 feet d. 35.2 feet

Explanation:

Step1: Apply Pythagorean theorem

Let the height be $h$, the base be $a = 12.5$ ft and the hypotenuse be $c=32.5$ ft. The Pythagorean theorem is $a^{2}+h^{2}=c^{2}$, so $h=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 12.5$ and $c = 32.5$ into the formula: $h=\sqrt{32.5^{2}-12.5^{2}}=\sqrt{(32.5 + 12.5)(32.5-12.5)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).

Step3: Calculate values inside square - root

$(32.5 + 12.5)(32.5-12.5)=(45)\times(20)=900$.

Step4: Find square root

$h=\sqrt{900}=30$ ft.

Answer:

C. 30 feet