A ship travels from Akron A on a bearing of 030° to Belleville (B) 90km away. It then travels to comptin (C) which is 310km due east of Akron (A)
1. Calculate the nearest km, the distance between Belleville (B) and comptin (C)
Did you make a sketch?
Looks to me that you have a triangle ABC, with AB=30, AC=310 and angle A = 60 degrees
A clear case of the cosine law:
BC^2 = 30^2 + 310^2 - 2(30)(310)cos 60
= ....
All angles are measured CW from +y-axis.
Given: AB = 90km[30o], BA = 90km[30+180] = 90km[210o].
AC = 310km[90o].
BC = BA + AC = 90[210o] + 310[90o],
BC = (90*sin210+310*sin90) + (90*cos210+310*cos90)i,
BC = 265 - 78i = 276km[-74o] = 276km[106o]CW.
Part two of that same questions said : calculate to the nearest degree the measure of ABC
2. sinB/310 = sin60/276.
sinB = 310*sin60/276,
B =
294
To calculate the distance between Belleville (B) and Comptin (C), we need to use the Pythagorean theorem because the two locations form a right-angled triangle.
Step 1: Identify the two sides of the triangle
- Side BC represents the distance traveled from Belleville to Comptin, which is 310 km.
- Side AB represents the distance from Belleville to Akron, which is given as 90 km.
Step 2: Apply the Pythagorean theorem
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, BC is the hypotenuse, and AB and AC are the other two sides. We need to find AC.
AC^2 = BC^2 - AB^2
Substituting the values we have:
AC^2 = 310^2 - 90^2
AC^2 = 96100 - 8100
AC^2 = 88000
Step 3: Take the square root to find AC
AC = √88000
Calculating this square root would give us an approximate value, but since we only need the nearest kilometer, we can round it to the nearest whole number.
AC ≈ 296 km
Therefore, the nearest kilometer distance between Belleville (B) and Comptin (C) is approximately 296 km.