Trigonometry: Bearings Question?
Feeling like a bad tutor for not being able to fully solve this lol. In Q6 I’ve managed to find the triangle’s angle at the yacht corner, 92. I can’t seem to be able to find another side for the triangle in order to use cosine/sine rule.
For Q7 the two sides given (AB from Q6 and 1.2km is all I have :/
- SlowfingerLv 61 month agoFavourite answer
Draw a vertical line representing the coast, sea is to the right, land is to the left. A is down, B is up on that line. Point C representing the yacht is in the middle right. Connect the points. Angle in A is 90-32 = 58°. Angle in B is 300-270=30°
Angle in C is 180-58-30=92°.
We also know AB=2.2 km.
Use Law of Sines:
AB/sin C=BC/sin A = AC/sin B
BC= AB sinA / sin C
BC= 2.2 sin 58° / sin 92°= 1.867 km
BC=1.9 km (rounded to 1 d.p.)
AC = AB sin B / sin C
AC = 2.2 sin 30° / sin 92°= 1.101 km
AC = 1.1 km (rounded to 1 d.p.)
BC = 1.2km
angle B = 315-270 = 45°
Law of Cosines
AC^2 = AB^2 + BC^2 - 2 AB BC cos B
AC^2 = 2.2^2 + 1.2^2 - 2*2.2*1.2*cos 45°
AC^2 = 2.546
AC= 1.6 (to 1 d.p.)
- King LeoLv 71 month ago
You have one side, 2.2km and one angle of 92°. This is not enough info you two angles or two sides in order to solve this problem