QuestionTo find the distance across a river, a surveyor laid off a distance on one side of the river. It is found that and . Find .
The distance across the river is m
(Simplify your answer. Do not round until the final answer. Then round to the nearest whole number as needed.)
Studdy Solution
STEP 1
1. The problem involves a triangle where and are angles, and is a known side.
2. The angle is .
3. The angle is .
4. The side is meters.
5. We need to find the distance .
STEP 2
1. Calculate the third angle of the triangle.
2. Use the Law of Sines to find the length of .
STEP 3
Calculate the third angle of the triangle using the angle sum property of triangles:
Substitute the given angles:
Convert the angles to decimal form for easier calculation:
Calculate:
STEP 4
Use the Law of Sines to find :
Substitute the known values:
Solve for :
Calculate the sines:
Substitute these values:
Round to the nearest whole number:
The distance across the river is:
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