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26 July, 17:59

A small forest fire is cited due north of a fire lookout tower on Pikes Peak. From a second tower located 12.6 miles due west of the first tower a Ranger observed that the fires is 49.5° east of duo North. How far is the fire from the tower Pikes Peak

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  1. 26 July, 18:06
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    10.76 miles

    Step-by-step explanation:

    The following figure can be drawn from the information given.

    We have to find the adjacent side which is between the given angle and 90 degrees.

    Tan formula will be applied

    Tan (anlge) = opposite/adjacent

    Opposite = 12.6

    Angle = 49.5°

    Adjacent = x

    Tan (49.5°) = 12.6/x

    x = 10.76 miles

    Therefore, the fire is 10.76 miles away from the tower Pikes Peak.

    !
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