Question

On a map, Orlando is 178 millimeters due south of Niagara Falls, Denver is 273 millimeters from Orlando, and Denver is 235 millimeters from Niagara Falls. Find the bearing of Denver from Orlando and from Denver to Niagara Falls

Answer 1

N 58.4 ° W

S 81.5 ° W

Explanation:

Answer 2

N 58.4 ° W

S 81.5 ° W

Explanation:

Applying the law of cosine which is as follows:

C ^ 2 = A ^ 2 + B ^ 2 - 2 * A * B * Cos (° A)

In the first case we know that:

C = 235

A = 178

B = 273

If we replace we have:

235 ^ 2 = 178 ^ 2 + 273 ^ 2 - 2 * 178 * 273 * Cos (° A)

55225 = 106213 - 97188 * Cos (° A)

Cos (° A) = (55225 - 106213) / - 97188

Cos (° A) = 0.525

° A = arc cos (0.525)

° A = 58.4 °

Which means that from Denver to Orlando there is a bearing of N 58.4 ° W

In the second case we have to:

C = 273

A = 178

B = 235

If we replace we have:

273 ^ 2 = 178 ^ 2 + 235 ^ 2 - 2 * 178 * 235 * Cos (° B)

74529 = 86909 - 83660 * Cos (° B)

Cos (° B) = (74529 - 86909) / - 83660

Cos (° B) = 0.148

° B = arc cos (0.525)

° B = 81.5 °

Which means that from Niagara Falls to Denver there is a bearing of S 81.5 ° W