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

Answer:

2.38 miles

Step-by-step 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 !