# 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?

### 3 Answers

- la consoleLv 72 months ago
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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- llafferLv 72 months ago
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)

- MorningfoxLv 72 months agoReport
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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