Question

Three groups go out hiking and the three groups go in off in their own direction to explore (Groups 1, 2, and 3). Your group gets lost.

Your Group 1 and you radio in to groups 2 and 3. This is what 2 and 3 say to you.

Group 2: “We can see your group and group 3, you have 42 degrees between you two.”

Group 3. “We can see your group and group 2, you have 110 degrees between you two. Also, there is 250 meters between us and group 2.”

How far away is your group from Group 3? What about from Group 1?

Answer 1

The given data is as below. Let us denote the points at which Group 1, Group 2 and Group 3 are present as A, B and C respectively. As 2 angles are given and sum of all 3 angles of the triangles is 180, third angle C is 180-42-110 = 180-152 = 28

We know from law of sines that below holds good

We know that a = 250. From the trignometric tables Sin A = Sin 28 = 0.4695, Sin B = Sin 42 = 0.6691 and Sin C = Sin 110 = 0.9397. Hence we have the below

Hence Group 1 and Group 3 are 356.38 meters apart and Group 1 and Group 2 are 500.37 meters apart.