Question

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? Answe

Answer 1

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