Question

select the correct answer from each drop - down menu.
in a city, broadway, main street, and water street all intersect to form a triangle. broadway is 2000 m from main street to water street, main street is 1800 m from broadway to water street, and water street is 1200 m from main street to broadway.
complete the statement below.
in the triangle formed by the three streets, the greatest angle is the one formed by the intersection of
the smallest angle is the one formed by the intersection of
(there are also reset and next buttons shown.)

Explanation:

Step1: Recall the triangle angle - side relationship

In a triangle, the larger the side opposite an angle, the larger the angle, and the smaller the side opposite an angle, the smaller the angle. This is based on the Law of Sines (\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)) or the basic geometric principle of triangle angle - side correspondence.

Step2: Identify the side lengths

We are given the following distances (which represent the lengths of the sides of the triangle formed by the three streets):

• Broadway to Main Street: \(2000\) m
• Broadway to Water Street: \(1800\) m
• Main Street to Water Street: \(1200\) m

Step3: Determine the largest and smallest sides and their opposite angles

• The largest side is \(2000\) m (Broadway to Main Street). The angle opposite this side is the angle formed by the intersection of Broadway and Water Street (because the side between Broadway and Main Street is opposite the angle at Water Street).
• The smallest side is \(1200\) m (Main Street to Water Street). The angle opposite this side is the angle formed by the intersection of Broadway and Main Street (because the side between Main Street and Water Street is opposite the angle at Broadway).

Answer:

The greatest angle is the one formed by the intersection of Broadway and Water Street. The smallest angle is the one formed by the intersection of Broadway and Main Street.