University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2022
Views:

242

Pages:

8
Author:

5CelestialChronicle

Problem Solving Station #1 A ramp is used to load a 4-wheeler onto a truck bed that is 3 feet above the ground. The angle that the ramp makes with the ground is 32°. What is the horizontal distance covered by the 1 ramp? Round to the nearest hundredth. Solution: tan(32°) = 3/x x * tan(32°) = 3 x = 3 / tan(32°) x ≈ 4.80 ft Problem Solving Station #2 Find the perimeter of the triangle. Round to the nearest hundredth. right triangle with sides labeled 4.2 cm, x, and 18 cm Solution: sin(18°) = x / 4.2 x = 4.2 * sin(18°) x ≈ 1.30 cm cos(18°) = y / 4.2 y = 4.2 * cos(18°) y ≈ 3.99 cm Perimeter = 1.30 + 3.99 + 4.2 = 9.49 cm Problem Solving Station #3 A right triangle has an angle that measures 55°. The leg adjacent to this angle has a length of 43 cm. What is the length of the other leg of the triangle? Round to the nearest tenth. tan(55°) = x / 43 43 * tan(55°) = x x ≈ 61.4 cm Problem Solving Station #4 The hypotenuse of a right triangle measures 9 inches, and one of the acute angles measures 36°. What is the area of the triangle? Round to the nearest square inch. sin(36°) = y / 9 y = 9 * sin(36°) y ≈ 5.29 in cos(36°) = x / 9 x = 9 * cos(36°) x ≈ 7.29 in A = 1/2 * b * h = 1/2 * (5.29) * (7.29) ≈ 19 in² Problem Solving Station #7 What is EF, the measure of the longest side of the sail on the model? Round to the nearest inch. right triangle with hypotenuse EF, one leg FG = 28 inches, and angle F = 65 degrees sin(65°) = 28 / EF EF * sin(65°) = 28 EF = 28 / sin(65°) EF ≈ 30.89 inches ≈ 31 inches Problem Solving Station #8 Right triangle ABC is graphed on the coordinate plane and has vertices at A(-1, 3), B(0, 5), and C(4, 3). What is the measure of ∠C to the nearest degree? right triangle ABC on a coordinate plane AC = √((-1-4)² + (3-3)²) = √(-5)² = 5 BC = √((0-4)² + (5-3)²) = √(16+4) = √20 = 2√5 cos(∠C) = 2√5 / 5 ∠C = cos⁻¹(2√5 / 5) ∠C ≈ 27°