Question

Question :

Answer 1

Answer:

C) 405.3 ft

Step-by-step explanation:

A triangle is a polygon with three angles and three sides. Types of triangle are scalene, isosceles, equilateral, right angled triangle.

Given a triangle with angles A, B, C and the corresponding sides directly opposite to the angles as a, b, c. The sine rule states that:

$\frac{a}{sin(A)}= \frac{b}{sin(B)} =\frac{c}{sin(C)}$

In the triangle formed by point C, ship B and ship A, we have ∠A = 82°, ∠B = 78°, c = AB = 140 ft. Hence:

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

82 + 78 + ∠C = 180

∠C + 160 = 180

∠C = 20°

Using sine rule:

$\frac{c}{sin(C)}=\frac{a}{sin(A)}\\\\\frac{140}{sin(20)}=\frac{a}{sin(82)}\\\\a= \frac{140*sin (82)}{sin(20)}\\\\a=405.3\ ft$

a =  distance from Ship B to the signal fire at point C