Town Y is 9 km due north of town Z. Town X is 8km from Y, 5km from Z and somewhere to the west of the line YZ.
A) Draw triangle XYZ and find angle YZX
B) During an earthquake , town X moves due south until it is due west of Z. Find how far it has moved.
Hello, <3<3!
I assume you made sketches . . .
Town is 9 km due north of town
Town is 8km from , 5km from and somewhere to the west of the line
A) Draw and findCode:* Y * | 8 * | * | * | 9 * | X * | * | 5 * θ | * | * Z
Let
Law of Cosines: .
Therefore: .
B) During an earthquake, town moves due south until it is due west of
Find how far it has moved.Code:* Y * | 8 * | * | * | 9 * | X * 5 | : * 62.2°| : * | : 27.8° * | W * - - - - - * Z
Town has moved directly south to
Since , then: .
In right triangle
Therefore, town moved about 2.3 km.