This is a right triangle
(BD)^2 = 7^2+8^2
(DC)^2 = 16^2 +8^2
Can you finish from here??
(BD)^2 = 7^2+8^2
(DC)^2 = 16^2 +8^2
Can you finish from here??
1. Draw a diagram: Start by drawing a diagram representing the given locations A, B, C, and D. For convenience, put A at the origin (0,0) on a coordinate system.
D
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B--A--C
2. Determine the coordinates: Based on the information given, we can determine the coordinates of each village:
- A: (0,0)
- B: (0, -7) (since B is 7km due south of A)
- C: (0, -7 - 9) = (0, -16) (since C is 9km due south of B)
- D: (8, 0) (since D is due east of B)
3. Find the distances DB and DC:
- DB: To find the distance between D and B, we can use the distance formula:
DB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates for D (8,0) and B (0, -7):
DB = sqrt((8 - 0)^2 + (0 - (-7))^2)
= sqrt(64 + 49)
= sqrt(113)
≈ 10.63 km
- DC: Similarly, to find the distance between D and C:
DC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates for D (8,0) and C (0, -16):
DC = sqrt((8 - 0)^2 + (0 - (-16))^2)
= sqrt(64 + 256)
= sqrt(320)
≈ 17.89 km
So, DB is approximately 10.63 km and DC is approximately 17.89 km.