Question

Two cargo ships spot a signal fire on a small island. The captains know they are 140 feet

away from each other and using angle measuring device they can determine the angle from
cach of their ships to the signal fire. The angle at ship A is 82º and the angle at ship B is 78°.
How far is it from Ship B to the signal fire at point C?
Hint: Use Law of Sines:
sin A = sinB = sin C
82
B
a.
b.
48.9 feet
400.4 feet
c. 405.3 feet
d. 673.4 feet

Answer 1

`\large \boxed{\text{c. 405.3 ft}}`

Explanation:

`\begin{array}{rcr}\angle A + \angle B + \angle C & = & 180^(\circ)\\82^(\circ) + 78^(\circ) +\angle C & = & 180^(\circ)\\160^(\circ) + \angle C & = & 180^(\circ)\\\angle C & = & 20^(\circ)\\\end{array}`

`\begin{array}{rcl}(\sin A)/(a) & = &(\sin C)/(c)\\\\(\sin82^(\circ))/(a) & = &(\sin20^(\circ))/(140)\\\\(0.9903)/(a) & = &(0.3420)/(140)\\\\a & = & (0.9903 *140)/(0.3420)\\\\& = & \mathbf{405.3 ft}\\\end{array}\\\text{The distance from Ship B to the signal fire is $\large \boxed{\textbf{405.3 ft}}$}`