Solve the problem.
-Avegail needs to determine the distance at certain points across a lake. Her crew and she are able to measure the distances shown on the diagram below. Find how wide the lake is to the nearest tenth of a meter.
A)115.3 m
B)8.4 m
C)143.2 m
D)70 m

Question

Solve the problem.
-Avegail needs to determine the distance at certain points across a lake. Her crew and she are able to measure the distances shown on the diagram below. Find how wide the lake is to the nearest tenth of a meter. 
A)115.3 m 
B)8.4 m 
C)143.2 m 
D)70 m

Quizplus · Accepted Answer

By using the Pythagorean theorem, we can solve for the width of the lake. We can see that the measurements given form a right triangle, where the distance across the lake is the hypotenuse. Using the measurements given, we have:

$(D+80)^2 = (D-20)^2 + 96^2$

$D^2 + 160D + 6400 = D^2 - 40D + 400 + 9216$

$200D = 11816$

$D \approx 59.08$

Therefore, the width of the lake is approximately 59.08 - 20 = 39.08 meters. Rounded to the nearest tenth, the answer is 39.1 meters, which corresponds to choice letter A.

Solve the Problem. -Avegail Needs to Determine the Distance at Certain Points Across