Transcript Lesson 12.3

Section 12-3

The Law of Sines enabled you to find the
lengths of sides of a triangle or the measures
of the angles in certain situations. To use the
Law of Sines, you needed to know the
measures of two angles and the length of any
side, or the lengths of two sides and the
measure of the angle opposite one of the
sides. What if you know a different
combination of sides and angles?

Two hot-air balloons approach a landing
field. One is 12 m from the landing point and
the other is 17 m from the landing point. The
angle between the balloons is 70°. How far
apart are the two balloons?

Sketch one altitude to form two right
triangles, so that one of the right triangles
contains the 70° angle.

Sketch one altitude to form two right
triangles, so that one of the right triangles
contains the 70° angle.

The towns of Easton and Westville lie on
opposite sides of a mountain. The
townspeople wish to have a tunnel
connecting the towns constructed through
the mountain. A construction engineer
positions herself so that she can see both
towns. She plans to make some
measurements and use trigonometry to
determine the length of the proposed tunnel.

In this investigation you will
simulate this situation. Position
three members of your group so
that two people are on opposite
sides of a wall and the third
person can see both of them.
The first two group members
represent the two towns, and
the wall represents the
mountain. The third member
represents the engineer. Find
the distance between the two
towns. Sketch an overhead view
of the situation, show the
measurements you make, and
show your calculations.

Find the unknown angle measures and side
lengths.