You and a friend are out hiking across a large flat plain and decide to determin
ID: 1691547 • Letter: Y
Question
You and a friend are out hiking across a large flat plain and decide to determine the height of a distant mountain peak, and also the horizontal distance from you to the peak. In order to do this, you stand in one spot and determine that the sightline to the top of the peak is inclined at 7.5° above the horizontal. You also make note of the heading to the peak at that point: 13° east of north. You stand at the original position, and your friend hikes due west for 1.5 km. He then sights the peak and determines that its sightline has a heading of 15° east of north. How far is the mountain from your position, and how high is its summit above your position? You and a friend are out hiking across a large flat plain and decide to determine the height of a distant mountain peak, and also the horizontal distance from you to the peak. In order to do this, you stand in one spot and determine that the sightline to the top of the peak is inclined at 7.5° above the horizontal. You also make note of the heading to the peak at that point: 13° east of north. You stand at the original position, and your friend hikes due west for 1.5 km. He then sights the peak and determines that its sightline has a heading of 15° east of north. How far is the mountain from your position, and how high is its summit above your position?Explanation / Answer
Since they don't give you the incline as seen by your friend they must be looking for an approximate solution. Let d1 be the distance of you from the peak and d2 the distance of your friend from the peak (measured horizontally) Using the law of cosines d1^2 + d2^2 - 2 d1 * d2 cos 2 = 1.5^2 = 2.25 The separation of you and your friend are also 2 deg as seen from peak Since d1 equals approximately d2 then .0006 d^2 = 2.25 / 2 d = 43.3 km h/d = tan 7.5 h = 5.7 km = 5700 m
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