Question

a Gardner has decided to build a fence around her garden. her garden happens to be shaped perfectly like right triangle. the hypotenuse of her garden measures 80 feet long and the side next to the hypotenuse measures 65.532 feet long. those two sides of the garden form a 35 degree angle between them. if the Gardner has ordered 185 feet of fence,will she have enough?

Answer 1

hypotenuse of triangle, = 80 feet

let the side next to hypotenuse be base = 65.532 feet

Therefore, the remaining side can be calculated using pythagoras theorem as garden is perfectly right triangle.

(hypotenuse)2 = (base)2 + (perpendicular)2

(80)2 =(65.532)2 + (x)2

x2 = 6400 - 4294.4430

x2 = 2105.557

x = 45.886 feet

So, the perimeter of the triangle is ( 80 + 65.532 + 45.886) = 191.418 feet

Since, the perimeter of the triangle is more than the length of the ordered fence which is 185 feet. Therefore, there will not be enough fence, (191.418 - 185 ) = 6.418 feet of fence will be more needed.