consider a right triangle PQR, with Q=90°. p = q sinP
So, in any other triangle, if given p,q, and P
if p < q sinP, then it is too short to meet side r, so no triangle possible
If p > q sinP, then there will be two triangles, one obtuse and one acute.
So, for problem a above, since 3 > 5 sin27°, there are two triangles that work
See what you can do with the others.
For each of the following, tell how many non congruent triangles PQR fit the given description, and find the size of angle Q. Make a separate diagram for each case. (a) p = 3, q = 5, angle P = 27 degrees (b) p = 8, q = 5, angle P = 57 degrees (c) p = 7, q = 8, angle P = 70 degrees (d) p = 10, q = 20, angle P = 30 degrees.
1 answer
1 answer