Triangle PQR is a 30-60-90 triangle with right angle Q and longer leg PQ. Find the possible coordinates of R i

Question

Triangle PQR is a 30-60-90 triangle with right angle Q and longer leg PQ. Find the possible coordinates of R if P(-4,1) and Q(6,1). Hint: There are two solutions.

Answer 1

The answers are (6, 1 + L) and (6, 1 - L), where L is the length of side QR.

You can see that if you draw a picture/graph.

And since you know PQ is 10, you can figure out L using trigonometry. :) (Hint: The tangent function)

Answer 2

to respond to this actual, you ought to understand how the ratios between the legs artwork. For a 30-60-ninety triangle, the ratio is a million: SQRT(3): 2. certainly, you've 4 triangles. besides, understanding this ratio, you could illustrate the triangle and locate the relative place of the coordinates you're searching for. R? R? | | P-------Q | | R? R? here, we are able to make certain the prospective positions of R. considering that PQ is the longer leg, it follows that attitude R is 60 levels and attitude P is 30 levels. because of the fact the ratio is a million is to SQRT 3 (for the legs), we are able to compute the scale of the fast leg. PQ is length 10 (you could actual confirm this). to that end, the scale of the shorter leg is 10/SQRT(3) = 10 SQRT(3) / 3. you're R could have those coordinates: (-4, a million + 10SQRT(3)/3 ) (-4, a million - 10SQRT(3)/3 ) (6, a million + 10SQRT(3)/3 ) (6, a million - 10SQRT(3)/3 ) desire you recognize this.