There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of B, 7 miles away. What is the bearing needed to n…

Question

asked Oct 27, 2021 114k views

1 Answer

Bhurlow · Answer 1 · 2021-11-02T19:35:24+0000

Answer:

B = 38

Explanation:

This question can be illustrated using the attachment and the required bearing will be calculated using cosine theorem;

$b^2 = a^2 + c^2 - 2ac\ CosB$

In this case:

b = 5

a = 7

c = 8

<B = ??

Substitute these values in
$b^2 = a^2 + c^2 - 2ac\ CosB$

$5^2 = 7^2 + 8^2 - 2 * 7 * 8\ CosB$

$25 = 49 + 64 - 112\ CosB$

$25 = 113- 112\ CosB$

Collect Like Terms

$25 -113=- 112\ CosB$

$-88=- 112\ CosB$

Divide through by -112

$(-88)/(-112)= (- 112\ CosB)/(-112)$

(-88)/(-112)= CosB

Reorder

$Cos\ B = (-88)/(-112)$

$Cos\ B = 0.7857$

Take arccos of both sides

B = cos^(-1)(0.7857)

B = 38 --- (approximated)

Hence, the bearing is approximately 38 degrees