Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

# Trigonometry help needed!?

A cyclist travels 6.5 kilometres on a mountain road with a constant incline. After reaching the top of the road, he realizes that the mountain height is 1.1 kilometres. What is the angle of elevation for the road? Relevance
• sin θ = 1.1/6.5

θ = 9.743°

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• The required angle is β. According to the trigonometry rules:

6.5 * sin(β) = 1.1

sin(β) = 1.1/6.5

sin(β) ≈ 0.16923

β ≈ 9.743 °

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• Sine is the ratio between the opposite length of the angle over the hypotenuse in right triangles.  We can use that to solve for the unknown angle:

sin(x) = 1.1 / 6.5

sin(x) = 0.16923

I had to round above, but I didn't in my calculator to reduce errors due to rounding:

x = 9.743° (rounded to 3DP)

• Since the numbers in the problem have only two digits, the angle could be 9.22 degrees, 10.27 degrees, or anything in-between.

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