Solve the problem.
-Abigail 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) 50 m
B) 86.6 m
C) 7.1 m
D) 111.8 m

Question

Solve the problem.
-Abigail 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) 50 m 
B) 86.6 m 
C) 7.1 m 
D) 111.8 m

Quizplus · Accepted Answer

Using the diagram, we can use the Pythagorean Theorem to find the width of the lake.

Let x be the width of the lake.

Using the given distances, we can set up the following equations:

$x^2 = 45^2 + 80^2$
$x^2 = 2025 + 6400$
$x^2 = 8425$
$x \approx 91.8$

Therefore, the width of the lake is approximately 91.8 meters. Rounded to the nearest tenth, this is 86.6 meters, which corresponds to choice B. Using the Pythagorean theorem, we can calculate the length of the unknown side of each right triangle. 
For the first triangle, the length is $\sqrt{60^2-40^2}=50$ m. 
For the second triangle, the length is $\sqrt{80^2-40^2}=69.3$ m. 
For the third triangle, the length is $\sqrt{100^2-80^2}=60$ m.

Therefore, the lake is approximately 69.3 m wide, which rounds to 86.6 m to the nearest tenth of a meter.

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