Question

How much material is needed for the right triangular sail on a sailboat with a height of 4.5 m and hypotenuse of

5.5 m? Round your answer to the the nearest tenth of a meter squared.

Answer 1

The Pythagorean Theorem

If $a$  and $b$  are the lengths of the legs of a right triangle and $c$ is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse

$$c^2=a^2+b^2$$

Given $a=4.5m, c=5.5 m$

Find the length of the second leg $b$

$$b=\sqrt{c^2 -a^2 }$$

The area of the right triangle

$$Area=\dfrac{1}{2}ab$$

$$Area=\dfrac{1}{2}a\sqrt{c^2 -a^2 }$$

Substitute

$$Area=\dfrac{1}{2}(4.5m)\sqrt{(5.5m)^2 -(4.5m)^2 }\approx7.1m^2$$

7.1 square meters of material is needed for the right triangular sail on a sailboat with a height of 4.5 m and hypotenuse of 5.5 m.