Jasmin has a shelving unit that has 3 surfaces that are scalene trinagles. She wants to put shelf paper on each surface, and so needs to determine how much to buy. 2 of the the sides have lengths of 22 inches and 35 inches, and the angle formed between them is 87 degrees. To the nearest square inch, how much paper is needs for all 3 shelves?
To the nearest square inch, Jasmin needs to buy 1,153 square inches of shelf paper. Answer: 1,153 inches²
To solve for the area of one surface of the shelving unit, we use the formula for the area of a scalene triangle:
Area = 1/2 * base * height
Given that the two sides with lengths of 22 inches and 35 inches form an angle of 87 degrees, we can use the Law of Cosines to find the length of the third side (base):
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the length of the third side (base), a is the first side (22 inches), b is the second side (35 inches), and C is the angle between the two sides (87 degrees).
Substituting in the given values:
c^2 = 22^2 + 35^2 - 2*22*35*cos(87)
Now we can solve for c:
c^2 = 484 + 1225 - 1540*cos(87)
c^2 = 1709 - 1540(-0.087)
c^2 = 1709 + 133.48
c^2 = 1842.48
c ≈ √(1842.48)
c ≈ 42.97
Now we have all three side lengths of the triangle: 22 inches, 35 inches, and 42.97 inches.
We can now find the area of one surface using the formula:
Area = 1/2 * base * height
where the base is 22 inches and the height is the length of the third side (42.97 inches):
Area = 1/2 * 22 * 42.97
Area ≈ 469.34 square inches
Since there are three surfaces, we need to buy 469.34 * 3 = 1408 square inches of shelf paper. Rounding to the nearest square inch, Jasmin needs to buy 1408 square inches of shelf paper. Answer: \boxed{1408}.
options are:
660 inches²
660 inches²
1,153 inches²
1,153 inches²
1,647 inches²
1,647 inches²
2,038 inches²
2,038 inches²