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25 November, 02:43

Due to construction, traffic is getting detoured from Main Street by turning slightly right onto Oak Avenue and continuing straight for 4 mi. To get back onto Main Street, you need to make a 90 degree left turn onto Lilac Lane and continue straight for x miles. Lilac Lane intersects Main Street at 30 degrees for the end of the detour. Approximately how many miles should you travel on Lilac Lane to reach Main Street?

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  1. 25 November, 05:42
    0
    6.9 miles

    Assuming that Main Street, Oak Avenue, and Lilac Lane are all straight, you have a right 30/60/90 right triangle. I do object to the phrase "turning slightly right onto Oak" since I wouldn't consider a 60 degree turn to be "slight". But in any case, the short leg of the 30/60/90 triangle is the 4 miles given and the long leg will be sqrt (3) times longer. So

    sqrt (3) * 4 miles = 1.732050808 * 4 miles = 6.92820323 miles

    So you would need to travel about 6.9 miles on Lilac Lane to reach Main Street.
  2. 25 November, 06:16
    0
    For this case you should see the problem as a rectangle triangle whose sides are 4 miles (base) and x miles (height).

    the angle between the hypotenuse and the base is 30 degrees.

    then to find the height:

    tan (30) = x / 4

    x = 4 * tan (30) = 2.31

    answer

    you should travel 2.31 miles on Lilac Lane to reach Main Street
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