Question

Ikyume is 62m away from Amadi, on a bearing of 012°. Becky is 42m away from Ikyume and on bearing of 082°. How far is Amadi from Becky, and on what bearing?

Answer 1

Amadi is 86m far from Becky

Amadi is on the bearing of 78° .

Explanation:

From the information given ,

let I represent Ikyume

A represent Amadi and B represent Becky

From the information in the diagrammatic expression shown below:

Using cosine rule;

i² = a² + b² - 2ab cos (I)

i² = 42² + 62² - 2(42×62) cos (110°)

i² = 1764 + 3844 - 5208 (- 0.342)

i² = 1764 + 3844 - ( - 1781.136)

i² = 1764 + 3844 + 1781.136

i² = 7389.136

i =
`\mathtt{√(7389.136)}`

i = 85.96

i
`\simeq` 86 m

Amadi is 86m far from Becky

From point I , 12° = 12° at point A (alternate angles)

In that quadrant = 90 - 12° = 78°

Therefore, Amadi is on the bearing of 78° .