Respuesta :
Answer:
The two possible distances from Ship A to the distress call boat are 64.4 km and 147.5 km
Step-by-step explanation:
The given parameters are;
The distance between Ship A and Ship B = 120 km
The distance of the distress call from Ship B = 70 km
The angle made between the line from Ship A to B and the line from Ship A to the distress call = 28° = Opposite angle to the line from the location of the distress caller to Ship B
Therefore;
70/(sin(28°)) = 120/(sin(x))
Where;
x = The angle opposite the line from Ship A to B
sin(x) = ((sin(28°))×120)/70 = 0.805
x = sin⁻¹(0.805) = 53.59°
Therefore, the angle opposite the line from Ship A to the distress caller, r = 180 - (28 + 53.59) = 98.4°
From sin rule, we have;
70/(sin(28°)) = r/(sin(98.4°))
r = (70/(sin(28°)))×(sin(98.4°)) = 147.5
However by cosine rule, we have;
70² = 120² + r² - 2×120×r × cos(28°)
4,900 = 14,400 + r² - 211.907·r
r² - 211.907·r + 14,400 - 4,900 = 0
r² - 211.907·r + 9,500 = 0
Factorizing, we have;
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
[tex]r = \dfrac{211.907\pm \sqrt{211.907^{2}-4\times 1\times 9,500}}{2\times 1}[/tex]
r = 64.406 km or 147.501 km
Which gives;
The distance of the line from Ship A to the distress caller = 64.4 km or 147.5 km to the nearest tenth.
The two possible distances from Ship A to the distress call boat = 64.4 km and 147.5 km
