Question

Swanson plans to attempt to swim across the lake from point A to point B as shown below. To determine how far he will have to swim, he has chosen a point C and calculated the labeled data.

How many miles will he have to swim? Round your answer to two decimal places.

Answer 1

Here is the answer :P

Answer 2

2.38 miles

Explanation:

From Given diagram:

In ΔABC,

AC=2.5 miles

BC= 3.7 miles

∠BCA= 39.4°

Now as we have two sides and an angle, using law of cosines to find the third side:

c= √(a^2+b^2-2abcosα

AB=√(AC)^2 + (BC)^2 - 2(AC)(BC)cosα

=√(2.5)^2 + (3.7)^2 - 2(2.5)(3.7)cos(39.4°)

=√(2.5)^2 + (3.7)^2 - 2(2.5)(3.7)(0.77)

=√(5.695)

= 2.38 !