Question

segitiga pqr dg sudut q=45drajat, sudut r=105 drajat, dn pq= (akar 6 + akar 2) cm. jika sin 105 drajat=1 per 4 (akar 6 + akar 2. tentukn pnjang:
a. qr
b. pr

Answer 1

QR :

sinR / PQ = sinP / QR
sin105 / √6 + √2 = sin(180 - 105 - 45) / QR
(1/4√6+√2) / (√6 + √2) = sin30 / QR
(1/4√6+√2) / (√6 + √2) = 1/2 / QR
1/4√6 + √2 QR = 1/2(√6 + √2)
(√6 + √2)/4 QR = (√6 + √2) / 2
QR = ((√6 + √2) / 2) / ((√6 + √2) / 4)
QR = 4 / 2
QR = 2 cm

==========

PR :

sinP / QR = sinQ / PR
sin30 / 2 = sin45 / PR
1/2 / 2 = 1/2√2 / PR
1/2PR = √2
PR = 2√2 cm

Answer 2

PR
PR: SinP / QR = SinQ / pr
sin30/2=sin 45/pr
1/2/2= 1/2√2/pr
1/2 pr = √2
PR: 2√2CM