A wheelchair ramp near the door of a building has an incline of 15 degrees and a run of 7.11 m from the door. Calculate the length of the ramp to the nearest hundredth of a metre
Angle of elevation is 15 degrees and we're trying to solve for the hypotenuse of the right triangle given the adjacent is 7.11 m.
We could use primary trig ratios to solve - COS.
Let x represent the length of the ramp (hypotenuse)
Cos15= ADJACENT/HYPOTENUSE
Cos15= 7.11/x
x=7.11/cos15
x=7.36 m
Therefore, the ramp is 7.36 m in length.
Well, let's see. If I were a ramp, I would try my best to be as long as possible. But in this case, the ramp has a 15-degree incline, which means it forms a right triangle with the ground. So to calculate the length of the ramp, we can use some trigonometry.
Now, I don't want to take away any joy from you, so I won't solve this problem like a boring bot. Instead, I'll calculate the length of the ramp using a bit of math comedy. Are you ready?
Drumroll please...
Using the magical powers of trigonometry and a dash of silliness, we can use the tangent function to solve this. The tangent of the angle is equal to the opposite side (the length of the ramp) divided by the adjacent side (the run).
So, tan(15) = Ramp length / 7.11
Now, let's bring out our calculator hats and solve this equation. By rearranging the equation, we get:
Ramp length = tan(15) x 7.11
And after some calculations, the length of the ramp is approximately 1.97 meters. Ta-da!
Now, be sure to check the validity of this answer and take any necessary safety precautions before using the ramp. Safety is no joking matter!
To calculate the length of the ramp, we can use the trigonometric function tangent. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the ramp's height is the opposite side and the ramp's run is the adjacent side.
To find the length of the ramp, we can use the formula:
Length of Ramp = Height / sin(Angle)
First, let's find the height of the ramp using the given angle and run.
Height = run * sin(Angle)
Substituting in the given values, we have:
Height = 7.11 m * sin(15 degrees)
Using a calculator, we can calculate that sin(15 degrees) is approximately 0.2588.
Height = 7.11 m * 0.2588 = 1.838508 m
Now we can find the length of the ramp using the formula mentioned earlier:
Length of Ramp = 1.838508 m / sin(15 degrees)
Using a calculator, we can calculate that sin(15 degrees) is approximately 0.2588.
Length of Ramp = 1.838508 m / 0.2588 ≈ 7.10 m
Therefore, the length of the ramp, to the nearest hundredth of a meter, is 7.10 m.
To calculate the length of the ramp, we can use trigonometry. We know that the ramp forms a right angle triangle with the ground, where the angle of inclination is 15 degrees and the "run" is given as 7.11 meters.
In a right angle triangle, the ratio of the opposite side (height) to the adjacent side (run) is defined by the tangent function. In this case, we can use the tangent of 15 degrees to find the length of the vertical side (height) of the triangle.
The formula for calculating the length of the vertical side is:
height = run * tan(angle)
Plugging in the values, we have:
height = 7.11 * tan(15 degrees)
Now, we need to calculate the tangent of 15 degrees. Most calculators have a "tan" function, so you can simply input "tan(15)" to get the answer. However, if you don't have a calculator or want to know how to calculate it manually, you can use the following steps:
1. Convert the degrees to radians. To convert degrees to radians, multiply by π/180. So, 15 degrees is equal to 15 * π/180 radians.
2. Calculate the tangent of the angle using the radians. The tangent of an angle is equal to the ratio of the sine of the angle to the cosine of the angle. So, the tangent of 15 degrees is equal to sin(15 degrees) / cos(15 degrees).
3. Now, we can calculate the length of the vertical side (height). Multiply the run (7.11 m) by the tangent of 15 degrees to get the height.
Once you have the height, you can find the length of the ramp by using the Pythagorean theorem, which states that in a right angle triangle, the square of the hypotenuse (ramp) is equal to the sum of the squares of the other two sides (height and run).
length of ramp = √(height^2 + run^2)
Substituting the known values, you can calculate the length of the ramp to the nearest hundredth of a metre.