Ringo works on a road construction crew in the surveyors unit. He measures the angle of elevation of the road with an instrument called a theodolite, as shown. The angle of elevation from one point to another is 7.60. The slope distance between the two points on the road is 267.4 m.How many meters does the road rise over that distance?(Round your answer to the nearest 1 decimal place and put only the number in the box with no units.)
Question
Ringo works on a road construction crew in the surveyors unit. He measures the angle of elevation of the road with an instrument called a theodolite, as shown. The angle of elevation from one point to another is 7.60. The slope distance between the two points on the road is 267.4 m.How many meters does the road rise over that distance?(Round your answer to the nearest 1 decimal place and put only the number in the box with no units.)
Solution
To solve this problem, we need to use the concept of trigonometry. Specifically, we will use the sine function, which is defined as the ratio of the opposite side (the height we want to find) to the hypotenuse (the slope distance).
The formula we will use is:
sin(angle) = opposite/hypotenuse
We can rearrange this formula to solve for the opposite side (the height):
opposite = sin(angle) * hypotenuse
Substituting the given values:
height = sin(7.6) * 267.4
Before calculating, make sure your calculator is set to degrees, not radians.
After calculating, round your answer to the nearest 1 decimal place.
Let's calculate:
height = sin(7.6) * 267.4 = 35.4 meters
So, the road rises by approximately 35.4 meters over that distance.
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