Question

Sally is building a flower bed in the shape of a 30°-60°-90° triangle. The hypotenuse is 18 feet. How long is the longest leg? Sally is building a flower bed in the shape of a 30°-60°-90° triangle. The hypotenuse is 18 feet. How long is the longest leg? @Mathematics

Answer 1

longest leg would be the side opposite the 60 degree angle,
sine(60) = x/18
x = 18 * sine(60) = 18 sqrt3/2 = 9 sqrt3

Answer 2

The given triangle is a right angled triangle
and
In a right angled triangle, the hypotenuse is the longest side.

So, the longest leg is 18 ft..... (hypotenuse is given as 18 ft..)

Answer 3

\[18\text{Cos}[30{}^{\circ}]=9 \sqrt{3}=15.5885 \]

Answer 4

We need the "longest" side....
How can 15.5885 be longer than 18 ????????

Answer 5

15.5 feet is less than the hypotenuse which is given as 18 feet.

Answer 6

That is what I am saying...
The question asks "How long is the longest leg? "

so the correct answer is 18 ft.

Answer 7

Don't confuse "longest leg" with "longest side" The legs of a right triangle are the sides left when the hypotenuse is removed.