If a locomotive wheel with a diameter of 15 meters rolls 11.25 meters,through how many degrees and minutes does it turns?
what, no ideas of your own?
since one complete revolution (covering the distance of a circumference) is 2π radians, the angle subtended is
11.25/(15π)*2π = ? radians
then convert that to °&'
recall that s = rθ
Now just plug in your s and r to find θ (or a in your case)
Again, s = rθ, so plug in your s and r to find the central angle subtended by the base. Now, recall that the central angle is twice that of the triangle vertex subtending the base. I'll go ahead and finish this one up.
143.7 = 100θ
θ = 1.437 radians, or 82.33°
So, the vertex angle of the triangle is 41.17°
That means each of the base angles is (180-41.17)/2 = 69.42°
The last one is just like the 2nd one
The end of a pendulum of length 40cm travels an arc length of 5cm as it swings through an angle a.Find the measure of the central angle
An isoceles triangle is inscribed in a circle of radius 100 in.Find the angles of the triangle if its base subtends an arc of 143.7 inches?
Find the number of radians in the central angle that subtends an arc of 6m on a circle of diameter 5m?
1. Circumference = pi*D = 3.14 * 15 = 47.1 m.
11.25m/47.1m * 360deg. = 86.0 Deg.
3. Circumference = pi*D = 3.14 * 200 = 628 in.
Arc1 = Base(S1) = 143.7 in.
Arc2 = Arc3 = (628-143.7)/2 = 242.15 in. = S2 = S3. S1, S2, and S3 are the sides of the triangle.
Draw the altitude of triangle which bisects the base and forms two congruent rt. triangles.
Cos A = (0.5*143.7)/242.15 = 0.29672
A = 72.7o. = The base angles.
Vertex angle = 180-2*72.7 = 34.6o.
3. Corrections:
Circumference = pi*D = 3.14*200 = 628in
Arc1 = 143.7 in.
Arc1 = (143.7in/628in) * 360o = 82.4o.
Vertex angle = 82.4/2 = 41.2o.
Base angles = (180-41.2)/2 = 69.4o each
4. arc = 6m., D = 5m.
Ac = Central angle.
Circumference = pi*D = 3.14 * 5m = 15.7m.
Arc = (6m/15.7m) * 6.28radians = 2.4 radians.
Ac = Arc/Radius = 2.4/2.5 = 0.96 radians.
post it.
4. Correction: Ac = arc = 2.4 radians.
To find the number of degrees and minutes a locomotive wheel turns, we need to calculate the angle it rotates through.
First, let's determine the circumference of the wheel. The circumference of a circle is calculated using the formula: circumference = 2 * π * radius.
Given that the diameter of the wheel is 15 meters, we can determine the radius by dividing the diameter by 2:
radius = diameter / 2 = 15 / 2 = 7.5 meters.
Now, let's calculate the circumference:
circumference = 2 * π * radius = 2 * 3.14 * 7.5 ≈ 47.1 meters.
Next, we need to determine the fraction of the full rotation the wheel completes by rolling 11.25 meters. We can use the formula:
fraction = distance traveled / circumference.
fraction = 11.25 meters / 47.1 meters ≈ 0.239.
To convert this fraction into degrees, we need to multiply by 360 degrees, as a full circle is 360 degrees:
degrees = fraction * 360 ≈ 0.239 * 360 ≈ 86.04 degrees.
Since there are 60 minutes in one degree, we can calculate the minutes by multiplying the decimal part of the degrees by 60:
minutes = (0.04 * 60) ≈ 2.4 minutes.
Therefore, the locomotive wheel turns approximately 86 degrees and 2 minutes.