Angle of inclination

Find the angle of inclination of a ramp that rises 80 cm over a horizontal length of 200 cm.

Final Answer:

α =  23.5782 °

Step-by-step explanation:

y=80 cm l=200 cm  sin α = y:l  A=arcsin(y/l)=arcsin(80/200)≐0.4115 rad  α=A→  °=A⋅ π180​   °=0.4115⋅ π180​   °=23.578  °=23.5782∘=23°34′41"

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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:

Given:


- Rise (opposite side, opp ): 80 cm
- Length (hypotenuse, hyp ): 200 cm

Step 1:

Identify the Trigonometric Function
We can use the sine function, which relates the opposite side and the hypotenuse in a right triangle:
sin(θ) = oppositehypotenuse = 80200

Step 2:

Simplify the Ratio
sin(θ) = 80200 = 25 = 0.4

Step 3:

Find the Angle θ
To 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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