A 60m long bridge has an opening in the middle and both sides open up to let boats pass underneath. The two parts of the bridge floor rise up to a height of 18 m. Through what angle do they move?
sin(Θ) = 18 / 30
Imagine the bridge to be a huge right angled triangle . It it rises by 18 m then the this height is the opposite and the length of the bridge is the hypotenuse . Now, apply sin theta ( hope , u know this ) using the SOH CAH TOA rule we get that sin theta is 18 / 30 further simplifying we get 3/5 . Now, if u enter arc sin of 3/5 in your calculator you will approximately get 36.87 or 37 degrees as the answer . That's it .......
Well, that bridge sounds like it's doing some fancy yoga moves! To figure out the angle, let's use a little imagination.
Imagine those bridge parts as arms stretching up in the air, going "ta-da!" Now, if we draw a line from each end of the raised bridge parts to the center of the bridge, we'll have an isosceles triangle.
Since the two raised parts are 18 m high, and the whole bridge is 60 m long, each raised part is 30 m long.
Using a little trigonometry magic, we can find the angle. The formula to find an angle in an isosceles triangle is:
angle = 2 x arctan(height / (length/2))
Plugging in the values, we get:
angle = 2 x arctan(18 / (30/2))
angle = 2 x arctan(18 / 15)
angle ≈ 2 x arctan(1.2)
angle ≈ 2 x 47.16°
angle ≈ 94.32°
So, those bridge parts rise up at an angle of approximately 94.32 degrees. That's quite a sight to see!
To find the angle through which the two parts of the bridge floor move, we can use trigonometry.
Let's assume that the two parts of the bridge floor rise symmetrically from the midpoint of the bridge to a height of 18 m, forming two right-angled triangles.
The length of each side of the right-angled triangle can be represented by the hypotenuse, which is half of the length of the bridge floor, and the height, which is 18 m.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse of each triangle:
hypotenuse^2 = height^2 + base^2
where the base of each triangle is half of the length of the bridge floor.
The base can be calculated as half of 60 m, which is 30 m.
Let's substitute the values into the formula:
hypotenuse^2 = 18^2 + 30^2
hypotenuse^2 = 324 + 900
hypotenuse^2 = 1224
Taking the square root of both sides, we find:
hypotenuse ≈ 34.98 m
Now, we can find the angle, θ, by using the trigonometric function of sine:
sin(θ) = height / hypotenuse
Substituting the values, we get:
sin(θ) = 18 / 34.98
Using the inverse sine function, we can find the angle θ:
θ ≈ sin^-1(18 / 34.98)
θ ≈ 30.62°
Therefore, the two parts of the bridge floor move through an angle of approximately 30.62 degrees.
To find the angle through which the two parts of the bridge floor move, we can use trigonometry.
First, let's visualize the situation. We have a bridge that is 60 meters long with an opening in the middle. When boats pass underneath, the two parts of the bridge floor rise up to a height of 18 meters.
Now, let's consider one side of the bridge. We have a right triangle where the base is half of the bridge length (30 meters) and the height is 18 meters. We can use trigonometric functions to find the angle.
The tangent function relates the opposite side (height) to the adjacent side (base) in a right triangle. So we can use the inverse tangent (arctan) function to find the angle.
The formula to find the angle (θ) is:
θ = arctan (height / base)
In this case, the height is 18 meters, and the base is 30 meters. Let's calculate the angle.
θ = arctan (18 / 30)
θ ≈ 33.69 degrees
Therefore, both parts of the bridge floor move through an angle of approximately 33.69 degrees.