Answer:
1) a = 6.14 km
2) b = 4.69 km
Explanation:
Let the first building be A, second building be B and third building be C.
Now, bearing of A = 4.76 km in a direction 37° north of east
Bearing of B = 69° west of north
Bearing of C = 28° east of south
Thus if this 3 points form a triangle, we will have the following angles;
Angle at point A = 28 + (90 - 37) = 81°
Angle at point B = 28 + (90 - 69) = 49°
Angle at point C = 180 - (81 + 49) = 50°
Now, the distance between second and third building is "a" which is represented by BC in the triangle attached while the given distance of 4.76 represents side AB. Thus;
Using sine rule, we can find "a".
a/sin 81 = 4.76/sin 50
a = 6.14 km
B) distance between first and third building is AB in the triangle depicted by "b".
Similar to the first problem, we will use sine rule again.
b/sin49 = 4.76/sin 50
b = 4.69 km
