Angle of inclination
Find the angle of inclination of a ramp that rise for 80 cm and is 200 cm long.
Correct answer:

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Dr. Math
To find the angle of inclination θ of the ramp, we can use the trigonometric relationship involving the rise (opposite side) and the length (hypotenuse) of the ramp. Here's a step-by-step solution:
- Rise (opposite side, opp ): 80 cm
- Length (hypotenuse, hyp ): 200 cm
We can use the sine function, which relates the opposite side and the hypotenuse in a right triangle:
To find the angle whose sine is 0.4, we use the inverse sine function (sin-1):
Calculating this:
Given:
- Rise (opposite side, opp ): 80 cm
- Length (hypotenuse, hyp ): 200 cm
Step 1:
Identify the Trigonometric FunctionWe can use the sine function, which relates the opposite side and the hypotenuse in a right triangle:
sin(θ) = opposite/hypotenuse = 80/200
Step 2:
Simplify the Ratiosin(θ) = 80/200 = 2/5 = 0.4
Step 3:
Find the Angle θTo find the angle whose sine is 0.4, we use the inverse sine function (sin-1):
θ = sin-1(0.4)
Calculating this:
θ ≈ 23.58°
Final Answer
23.58°
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See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.
You need to know the following knowledge to solve this word math problem:
- algebra
- expression of a variable from the formula
- planimetrics
- right triangle
- triangle
- goniometry and trigonometry
- sine
- tangent
- arctangent
- arcsine
Units of physical quantities:
Grade of the word problem:
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