calculate the two possible values of angle qrp and the corresponding lengths of pr illustate answer with diagram please
2006-11-17 23:12:54 · 5 answers · asked by STUART A 1 in Science & Mathematics ➔ Mathematics
Use the sine law.
A/sin(a) = B/sin(b) = C/sin(c)
where angles a, b, c are opposite sides A, B, C respectively.
In your example 5/sin(prq)=4/sin(40)
sin(prq)=5(sin(40))/4=
(5/4)(.6428)=.803
sin^(-1)(.803)=53.4degrees and the sine is positive in the
2nd quadrant as well as the first so angle qrp may also be
180-53.4 = 126.6
So if it's 53.4 then angle pqr is 180-(53.4+40)=86.6
Again use the sine law to solve for pr.
pr/sin(86.6)=4/sin(40)
pr=4(sin(86.6))/sin(40)
pr=4(.998)/.6428
pr=6.21
And if it's 126.6 angle pqr is 180-(126.6+40)=13.4
pr/sin(13.4)=4/sin(40)
pr=4(.232)/.6428
pr=1.44
2006-11-18 01:04:57 · answer #1 · answered by albert 5 · 0⤊ 0⤋
qpr = 40, prq = 53.46, rqp = 86.53
(sin40)/4 = sin(qrp))/5
sin(qrp) = 5*0.6427876/4 = 0.80348
qrp = 53.46
rqp = 180 - 40 - 53.46 = 86.53
rp = 4sin(86.53)/sin(40)
rp = 6.2115 cm
2006-11-18 00:00:29 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋
use the wollowing equation:
a*a = b*b + c*c - 2*b*c*cos(alpha) where a, b, c are sides of the triangle, alpha is the angle between b and c.
2006-11-17 23:19:48 · answer #3 · answered by Anonymous · 0⤊ 0⤋
draw a diagram, ill give u the answer
2006-11-17 23:22:18 · answer #4 · answered by Anonymous · 0⤊ 1⤋
how the heck are we suppossed to diagram?
2006-11-17 23:15:03 · answer #5 · answered by just browsin 6 · 0⤊ 0⤋