1. An airplane is flying at 36,000 feet directly above Lincoln, Nebraska. A little later the plane is flying at 28,000 feet directly above Des Moines, Iowa, which is 160 miles from Lincoln.
A.assuming a CONSTANT rate of descent, what was the angle of descent?
B. What is the mileage of the plane?
2.A map maker wants to know the angle of assent of a mountain, so she can have info for contour maps. She knows from previous studies that the mountain is 5000 feet tall. Using her pedometer and walking a straight path from bottom to top, she measured that she walked 7500 feet. what is the incline of the mountain?
3.A rain gutter is to be constructed of thin aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge of the sheet, the sheet is bent up at an angle "a". The final span of the top of the rain gutter after its bent needs to be 9 inches.
A. find angle a
B. Find the top to bottom height of the final rain gutter
4.A carptenter is preparing to put a roof on a garage that is 20'x40'X20' (width,length, height). A steel support beam 45' high is positioned in the center of the garage. to support the roof, another beam will be attached to the top of the center beam.
A. at what angle is the new beam?
B.`How long of boards should he cut for each beam?
6. If 3 sides of a right triangle are 3,4, and 5, find ALL angles of the triangle.
1. A. To find the angle of descent, we can use trigonometry. Since we know the height difference between Lincoln and Des Moines (36,000 - 28,000 = 8,000 feet) and the horizontal distance between them (160 miles), we can use the tangent function. The angle of descent, represented by θ, can be found using the formula tan(θ) = opposite/adjacent. In this case, the opposite side is the height difference (8,000 ft) and the adjacent side is the horizontal distance (160 miles = 160 * 5280 = 84480 ft). Therefore, tan(θ) = 8000/84480. Now you can use the inverse tangent function to solve for θ.
B. To find the mileage of the plane, we need to find the distance it traveled horizontally. Since we know the horizontal distance between Lincoln and Des Moines is 160 miles, this is the mileage of the plane.
2. To find the incline of the mountain, we can use trigonometry. The incline angle, represented by θ, can be found using the formula sin(θ) = opposite/hypotenuse. In this case, the opposite side is the height of the mountain (5000 ft) and the hypotenuse is the distance she walked (7500 ft). Therefore, sin(θ) = 5000/7500. Now you can use the inverse sine function to solve for θ.
3. A. To find the angle "a" of the bent aluminum sheet, we can use the properties of right triangles. Since the sheet is bent up to form a rain gutter with a final span of 9 inches, the length of the hypotenuse of the right triangle formed by the top and the height of the gutter can be found using the Pythagorean theorem. The hypotenuse is equal to the square root of (9^2 - 4^2). Now you can use the inverse tangent function to find angle "a" using the formula tan(θ) = opposite/adjacent.
B. To find the top to bottom height of the final rain gutter, the height of the gutter can be found using the sine function. Since we know the angle "a" and the length of the hypotenuse (the span of the top, which is 9 inches), we can use the formula sin(θ) = opposite/hypotenuse. Now you can solve for the opposite side, which is the height of the gutter.
4. A. To find the angle of the new beam, we can use trigonometry. The angle of the new beam, represented by θ, can be found using the formula sin(θ) = opposite/hypotenuse. In this case, the opposite side is half the width of the garage (20/2 = 10 ft) and the hypotenuse is the height of the steel support beam (45 ft). Therefore, sin(θ) = 10/45. Now you can use the inverse sine function to solve for θ.
B. To find the length of each beam, we can use the Pythagorean theorem. The length of each beam can be calculated by using the formula sqrt((width/2)^2 + height^2).
6. Since the triangle is a right triangle with sides 3, 4, and 5, we can use the inverse sine, cosine, and tangent functions to find the angles. The sine of the angle opposite the side with length 3 can be found using sin(θ) = opposite/hypotenuse, which gives sin(θ) = 3/5. Similarly, we can find the other two angles using the same process.