Question

The post office is at the corner of the first Street and Main Street, which forms a right angle. First Street intersects with Oak Street to the north, and Main Street intersects with oat Street to the east. The intersection of the first Street and Oak Street forms an x angle, and tan x = 7/5. Car A drives on First Street for 10 miles to arrive at Oak street. How far will car B have to travel in Main Street to get to Oak Street? Round your answer to the nearest hundredth of a mile.

A) 28.14
B) 20
C) 14
D) 7.14

Answer 1

C) 14

Explanation:

Given the street geometry shown in the attachment with tan(x) = 7/5, you want to know the distance Car B drives on Main Street to get from the Post Office to Oak Street.

Tangent

The tangent ratio is given by ...

Tan = Opposite/Adjacent

In this geometry, this means ...

tan(x) = BP/AP = 7/5

Car B

Then the distance Car B drives is ...

BP = AP·7/5 = 10(7/5) = 14

Car B has to travel (C) 14 miles to get to Oak Street.

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