Answer:
0.69473828 radians east of north.
Step-by-step explanation:
Interpreting the information given on a Cartesian plane, the position of the ship will be (1,0) and that of the rock will be (7,5). Connecting the point (1,0) and (7,5) with a line and dropping a perpendicular line from point (7,5) to the x-axis to intersect the x-axis at (7,0), will form a right-triangle with base length 6 units and a height of 5 units.
<u>Finding the base length from points (1,0) and (7,0)</u>
d=√(x₂-x₁)²+(y₂-y₁)²
d=√(7-1)²
d= √6²
d=6 units
<u>Finding the height from points (7,5) and (7,0)</u>
d=√(x₂-x₁)²+(y₂-y₁)²
d=√(7-7)² + (0-5)²
d=√-5²
d=√25
d=5 units
So you now have a right triangle with base length 6 units and height 5 units.
To get the bearing of rock from ship position you apply the formula for tangent of an angle
Tan Ф = length of opposite side/length of adjustment side
TanФ=5/6
Tan Ф =0.83333333333
Tan⁻¹ (0.83333333333) =0.69473828 radians east of north.
