Using Trigonometry to Find Side Lengths of an Acute Triangle
a. Find the lengths of 𝑑 and 𝑒.
b. Find the lengths of 𝑥 and 𝑦. How is this different from part (a)?
A surveyor needs to determine the distance between two points 𝐴 and 𝐵 that lie on opposite banks of a river. A point 𝐶 is chosen 160 meters from point 𝐴, on the same side of the river as 𝐴. The measures of ∠𝐵𝐴𝐶 and ∠𝐴𝐶𝐵 are 41° and 55°, respectively. Approximate the distance from 𝐴 to 𝐵 to the nearest meter.
Our friend the surveyor from Example 1 is doing some further work. He has already found the distance between points 𝐴 and 𝐵 (from Example 1). Now he wants to locate a point 𝐷 that is equidistant from both 𝐴 and 𝐵 and on the same side of the river as 𝐴. He has his assistant mark the point 𝐷 so that ∠𝐴𝐵𝐷 and ∠𝐵𝐴𝐷 both measure 75°. What is the distance between 𝐷 and 𝐴 to the nearest meter?
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