Chapter 8, Problem 15CT

To determine

The distance Madison needs to swim across Lake William, from the fishing lodge (point $A$ ) to the boat ramp (point $B$ ), if the distance of fishing lodge and intersect point of two roads (point $C$ ) is $3.5$ miles and the distance between boat ramp and intersect point of two roads (point $C$ ) is $4.2$ miles respectively and angle formed at point $C$ is ${32}^0$

  

Answer to Problem 15CT

Solution:

Madison needs to swim $2.2265$ miles.

Explanation of Solution

Given information:

  

The distance of the fishing lodge and intersect point of two roads (point $C$ ) is $3.5$ miles and

The distance between boat ramp and intersect point of two roads (point $C$ ) is $4.2$ miles

The angle formed at point $C$ is ${32}^0$

The points $A,B\text{and}C$ form a triangle $ABC$, where $BC=4.2$ miles, $AC=3.5$ miles and angle $C={32}^0$

By using cosine formula $c^2=a^2+b^2-2ab\cos C$

  $\Rightarrow c^2={\left(4.2\right)}^2+{\left(3.5\right)}^2-2\left(4.2\right)\left(3.5\right)\cos \left(32\right)$

  $\Rightarrow c^2=17.64+12.25-24.9326$

  $\Rightarrow c^2=4.9574$

  $\Rightarrow c=2.2265$

Therefore, Madison needs to swim $2.2265$ miles.