1. Joshua has a ladder that is 12 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.
The ceiling of Katie’s living room is a square that is 15 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 20 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work.
3. What is the area of to the nearest tenth of a square centimeter? Use special right triangles to help find the height. Show your work.
1) We have a right triangle.... Since we know the side opposite the angle and the hypotenuse, we can use the inverse sine (arcsin) to find the agle that the ladder makes
So we have...
arcsin (11.8 / 12) ≈ 79.5 ° [unsafe ]
2) The perimeter = 4(15) = 60 ft
The combined length of both diagonals = 2 * √2 * side length = 2 * √2 * 15 =
30 √2 ≈ 42.4 ft
So.....the total required = [ 60 + 42.4] / 20 = 5.12 rolls = 6 rolls
3) The triangle height = 5√3 cm
So....the area =
(1/2) base * height = (1/2) (5) (5√3) = (25/2)√3 ≈ 21.7 cm