Answer:
The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.
Step-by-step explanation:
Let the distance of the ship to coastguard P be represented by x, and its distance to coastguard Q be represented by y.
But,
<P = 048°
<Q = [tex]360^{o}[/tex] - [tex]324^{o}[/tex]
= 0[tex]36^{o}[/tex]
Sum of angles in a triangle = [tex]180^{o}[/tex]
<P + <Q + <S = [tex]180^{o}[/tex]
048° + 0[tex]36^{o}[/tex] + <S = [tex]180^{o}[/tex]
[tex]84^{o}[/tex] + <S = [tex]180^{o}[/tex]
<S = [tex]180^{o}[/tex] - [tex]84^{o}[/tex]
= [tex]96^{o}[/tex]
<S = [tex]96^{o}[/tex]
Applying the Sine rule,
[tex]\frac{y}{Sin P}[/tex] = [tex]\frac{x}{Sin Q}[/tex] = [tex]\frac{z}{Sin S}[/tex]
[tex]\frac{y}{Sin P}[/tex] = [tex]\frac{z}{Sin S}[/tex]
[tex]\frac{y}{Sin 48^{o} }[/tex] = [tex]\frac{17}{Sin 96^{o} }[/tex]
[tex]\frac{y}{0.74314}[/tex] = [tex]\frac{17}{0.99452}[/tex]
⇒ y = [tex]\frac{12.63338}{0.99452}[/tex]
= 12.703
y = 12.70 km
[tex]\frac{x}{Sin Q}[/tex] = [tex]\frac{z}{Sin S}[/tex]
[tex]\frac{x}{Sin 36^{o} }[/tex] = [tex]\frac{17}{Sin 96^{o} }[/tex]
[tex]\frac{x}{0.58779}[/tex] = [tex]\frac{17}{0.99452}[/tex]
⇒ x = [tex]\frac{9.992430}{0.99452}[/tex]
= 10.0475
x = 10.05 km
Thus,
the ship S is at a distance of 10.05 km to coastguard P, and 12.70 km to coastguard Q.
