Answer:
The two possible distance are 147.5km and 64.4km
Step-by-step explanation:
Given
See Attachment for Illustration
Required
Determine the possible distance of ship A from the boat
The distress is represented by X;
So, the question requires we calculate distance AX;
This will be done using cosine formula as follows;
[tex]a^2 = b^2 + x^2 - 2bxCosA[/tex]
In this case;
a = 70;
b = ??
x = 120
A = 28 degrees
Substitute these values in the formula above
[tex]70^2 = b^2 + 120^2 - 2 * b * 120 Cos28[/tex]
[tex]4900 = b^2 + 14400 - 2 * b * 120 * 0.8829[/tex]
[tex]4900 = b^2 + 14400 - 211.9b[/tex]
Subtract 4900 from both sides
[tex]b^2 + 14400 - 4900 - 211.9b = 0[/tex]
[tex]b^2 + 9500 - 211.9b = 0[/tex]
[tex]b^2 - 211.9b + 9500 = 0[/tex]
Solve using quadratic formula
[tex]\frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Substitute 1 for a; -211.9 for b and 9500 for c
[tex]b = \frac{-(211.9)\±\sqrt{(211.9)^2 - 4 * 1 * 9500}}{2 * 1}[/tex]
[tex]b = \frac{211.9\±\sqrt{44901.61 - 38000}}{2}[/tex]
[tex]b = \frac{211.9\±\sqrt{6901.61}}{2}[/tex]
[tex]b = \frac{211.9\±83.08}{2}[/tex]
This can be splitted to
[tex]b = \frac{211.9+83.08}{2}[/tex] or [tex]b = \frac{211.9-83.08}{2}[/tex]
[tex]b = \frac{294.98}{2}[/tex] or [tex]b = \frac{128.82}{2}[/tex]
[tex]b = 147.49[/tex] or [tex]b = 64.41[/tex]
[tex]b = 147.5km\ or\ b = 64.4km[/tex]
Hence, the two possible distance are 147.5km and 64.4km
