Two planks of length 1m and 1.2m against each other if the angle between the planks is 36 (a) how far apart are the bottom edge of the planks (b) what angle does the longer one make with the floor
(a) We can use trigonometry to find the distance between the bottom edges of the planks. Let x be the distance we want to find. Then we have:
sin(36) = x / 1.2
x = sin(36) * 1.2
x ≈ 0.72 m
Therefore, the bottom edges of the planks are about 0.72 meters apart.
(b) We can use trigonometry again to find the angle that the longer plank makes with the floor. Let θ be the angle we want to find. Then we have:
sin(θ) = 1 / 1.2
θ = sin⁻¹(1/1.2)
θ ≈ 49.5°
Therefore, the longer plank makes an angle of about 49.5 degrees with the floor.
To solve this problem, we can use the trigonometric functions sine, cosine, and tangent. We'll first solve for the distance between the bottom edges of the planks and then find the angle the longer plank makes with the floor.
(a) To find the distance between the bottom edges of the planks, we can use the sine function:
sin(θ) = opposite/hypotenuse
Let's label the longer plank as A (1.2m) and the shorter plank as B (1m). The angle between the planks is 36.
Using the sine function:
sin(36) = opposite/hypotenuse
sin(36) = distance between the bottom edges / 1.2
Rearranging the equation, we can solve for the distance between the bottom edges:
distance between the bottom edges = sin(36) * 1.2
Using a calculator, the distance between the bottom edges is approximately 0.748 meters.
(b) To find the angle the longer plank makes with the floor, we can use the cosine function:
cos(θ) = adjacent/hypotenuse
In this case, the adjacent side is the distance between the bottom edges (0.748m) and the hypotenuse is the length of the longer plank, 1.2m.
Using the cosine function:
cos(angle) = 0.748 / 1.2
Rearranging the equation, we can solve for the angle:
angle = arccos(0.748 / 1.2)
Using a calculator, the angle the longer plank makes with the floor is approximately 45.84 degrees.
To find the distance between the bottom edges of the planks, we can use trigonometry. Let's assume the longer plank is upright and the bottom of the shorter plank is touching the floor.
(a) To find the distance between the bottom edges, we need to determine the horizontal distance between the bottom edge of the longer plank and the bottom edge of the shorter plank.
We can use the sine function to calculate this distance. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the hypotenuse is the longer plank, and the side opposite the angle is the vertical distance between the bottom edges.
Let's call the horizontal distance we want to find 'x.'
sin(36 degrees) = x / 1.2
x = 1.2 * sin(36 degrees)
x ≈ 0.727 meters
Therefore, the bottom edges of the planks are approximately 0.727 meters apart.
(b) To find the angle the longer plank makes with the floor, we can use the cosine function. The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is the horizontal distance we just found, and the hypotenuse is the length of the longer plank.
Let's call the angle we want to find 'θ'.
cos(θ) = x / 1.2
cos(θ) = 0.727 / 1.2
θ = cos^(-1)(0.727 / 1.2)
θ ≈ 41.6 degrees
Therefore, the longer plank makes an angle of approximately 41.6 degrees with the floor.