Laiwan 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 70. The slope distance between the two points on the road is 240 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
Laiwan 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 70. The slope distance between the two points on the road is 240 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 (height) to the hypotenuse (slope distance) in a right triangle.
Given: Angle of elevation = 70 degrees Slope distance = 240 m
We want to find the height (h), which is the rise of the road.
The formula for sine is:
sin(angle) = opposite/hypotenuse
Rearranging the formula to solve for the opposite side (height), we get:
opposite = sin(angle) * hypotenuse
Substituting the given values into the formula:
h = sin(70) * 240
Now, calculate the value of sin(70) and multiply it by 240 to get the height.
Remember to round your answer to the nearest 1 decimal place.
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