Question

Scorpion Gulch Shelter is having a pumpkin sale for Halloween. The pumpkins will be displayed on a triangular region in the parking lot, with sides 45 ft, 75 ft, and 102 ft. Each pumpkin takes about 3 ft^2 of space.

(a) About how many pumpkins can the shelter display?
(b) Find the measure of the middle-sized angle.

Answer 1

A) 513 pumpkin

B) Ø = 42.2 degree

Explanation:

Given that the triangle are of sides 45 ft, 75 ft, and 102 ft.

Let's first calculate the semi perimeter s of the triangle

S = ( a + b + c )/2

S = ( 45 + 75 + 102 )/2

S = 222/2 = 111

Area = sqrt root( s(s-a)(s-b)(s-c))

Area = sqrt root (111(66)(36)(9))

Area = 1540.66 square feet

If each pumpkin takes about 3 ft^2 of space.

The shelter display 1540.66/ 3 = 513.55

513 pumpkin

The measure of the middle-sized angle can be obtained by using cosine formula

75^2 = 45^2+102^2-2(45)(102)cosØ

5625 = 12429 - 9180cosØ

9180cosØ = 12429 - 5625

CosØ = 0.74118

Ø = 42.2 degree