If Triangle ABC similar to Triangle PQR, y+z equals: a) 2+ root3 b) 4+3root3 C)4+root3 d) 3+4root3 (in the fig, the two triangles are drawn as right triangles, but they r nt right triangles. the ifo in the picture r: QP=z, PR=y, RQ+6, ANGLE R+ 30, BA= z, AC=4root3, CB=8, ANGLE C= 30)
Answers
Answered by
7
see diagram.
In ΔABC, use cosine rule:
AB² = BC² + AC² - 2 BC AC Cos∠ACB
=> z² = 8² + (4√3)² - 2* 8 * 4√3 * Cos 30°
= 112 - 96 = 16 as cos 30° = √3/2
z = 4 units
As ΔPQR is similar to ΔABC, the ratio of corresponding sides:
PR / QR = AC / BC
=> PR / 6 = 4√3 / 8
=> y = PR = 3 √3 units
y + z = 4 + 3 √3 units
In ΔABC, use cosine rule:
AB² = BC² + AC² - 2 BC AC Cos∠ACB
=> z² = 8² + (4√3)² - 2* 8 * 4√3 * Cos 30°
= 112 - 96 = 16 as cos 30° = √3/2
z = 4 units
As ΔPQR is similar to ΔABC, the ratio of corresponding sides:
PR / QR = AC / BC
=> PR / 6 = 4√3 / 8
=> y = PR = 3 √3 units
y + z = 4 + 3 √3 units
Attachments:
Similar questions