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

length of pq = 10
length of rq = 10 tan 30 = 5.8
co-ord of r is (6,6.8) or (6,-5.8)

Answer 2

to respond to this easily, 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. relatively, you've got 4 triangles. besides, understanding this ratio, you may illustrate the triangle and discover the relative place of the coordinates you're searching for. R? R? | | P-------Q | | R? R? right here, we are able to work out the obtainable positions of R. because PQ is the longer leg, it follows that perspective R is 60 levels and perspective 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 dimensions of the quick leg. PQ is length 10 (you may easily be sure this). as a consequence, the dimensions 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 ) wish you already know this.