Question

9. Using a GPS, two readings were taken from Mr. Maier's house. Longs Peak (in Rocky Mountain National Park) is 30.5 miles away at a bearing of N65°W. Pikes Peak (near Colorado Springs) is 80.6 miles away at a bearing of S13°E. Determine the distance between the two peaks.

Answer 1

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Step 01:

Data

Longs Peak = 30.5 miles N65°W

Pikes Peak = 80.6 miles S13°E

distance between the two peaks = ?

Step 02:

Diagram

Step 03:

Longs Peak = 30.5 miles N65°W

x1:

30.5 * Sen 65 = 27.64

y1:

30.5 * Cos 65 = 12.89

Pikes Peak = 80.6 miles S13°E

x2:

80.6 * Sen 13 = 18.13

y2:

80.6 * Cos 13 = 78.53

Step 04:

DIstance

`d\text{ = }\sqrt[]{(x2-x1)^(2)+(y2-y1)^(2)}`
`d=\sqrt[]{(18.13-27.64)^(2)+(78.53-12.89)^(2)}`

d = 66.3152

The answer is:

The distance between the two peaks is 66.32 miles