village b is 7km due south of village a and village c is 9km due south of b, village d is 8km from a and is due east of b. find the distance of d from b and c.
To find the distance of village d from village b, we can create a right-angled triangle with sides 7km and 8km. Using the Pythagorean theorem, we can calculate the distance:
d^2 = 7^2 + 8^2
d^2 = 49 + 64
d^2 = 113
d = √113
d ≈ 10.63km
Therefore, village d is approximately 10.63km from village b.
To find the distance of village d from village c, we need to calculate the distance between village c and village b, and then add it to the distance we found above.
Using the Pythagorean theorem again with sides 7km and 9km:
x^2 = 7^2 + 9^2
x^2 = 49 + 81
x^2 = 130
x ≈ √130
x ≈ 11.40km
Adding this distance to the distance we found earlier:
10.63km + 11.40km ≈ 21.03km
Therefore, village d is approximately 21.03km from village c.