Question

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

Explanation:

Step1: Identify the problem type

This is a right - triangle problem. We know the hypotenuse and one side, and we want to find the other side. We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs of the right - triangle. Let the height of the sail be $h$, the given side be $a = 12.5$ ft and the hypotenuse $c=32.5$ ft.

Step2: Apply the Pythagorean theorem

We can rewrite the Pythagorean theorem to solve for $h$: $h=\sqrt{c^{2}-a^{2}}$. 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 the values inside the square root

First, calculate $(32.5 + 12.5)(32.5-12.5)=(45)(20)=900$.

Step4: Calculate the square root

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

Answer:

C. 30 feet