Question

In tabelul de mai jos sunt elementele unui triunghi ABC, m(A)=90°. Completați tabelul, stiind ca dimensiunile segmentelor sunt masurate in centimetri: b) AB=18; AC=?; BC=30; sin B=?; sin C=?; cos B=?; cos C=?; tgB=?; tg C=?; ctg B=?; ctg C=?; c) AB=?; AC=21; BC=35 in continuare la fel ca la b la toate sub punctele<br />d)AB=24; AC=32; BC=?<br />e) AB=?; AC=27; BC=45<br />f) AB=30; AC=? BC=50<br />VA ROG DAU 100 PUNCTE<br /><br />​urgent in searasta dau coroana
va rog urgent dau coroana si 100 de puncte​ varog iau nota mica

Answer 1

sin = lungimea catetei opuse / ipotenuza

cos = lungimea catetei alaturate / ipotenuza

tg = lungimea catetei opuse / lungimea catetei alaturate

ctg = lungimea catetei alaturate / lungimea catetei opuse

Pitagora

ip² = c₁² + c₂²

b)

AB = 18 cm, BC = 30 cm

AC = √BC² - AB² = √900-324 = √576 = 24 cm

sinB = AC/BC = 24/30 = 4/5

sinC = AB/BC = 18/30 = 3/5

cosB = AC/BC = 18/30 = 3/5

cosC = AB/BC = 24/30 = 4/5

tgB = AC/AB = 24/18 = 4/3

tgC = AB/AC = 18/24 = 3/4

ctgB = AB/AC = 18/24 = 3/4

ctgC = AC/AB = 24/18 = 4/3

c)

AC = 21 cm, BC  = 35 cm

AB = √1225 - 441 = 28 cm

sin B = 21/35 = 3/5

sinC = 28/35 = 4/5

cosB = 28/35 = 4/5

cosC = 21/35 = 3/5

tgB = 21/28 = 3/4

tgC = 28/21 = 4/3

ctgB = 28/21= 4/3

ctgC = 21/28 = 3/4

f)

AB = 30 cm, BC = 50 cm

AC = √2500 - 900 = 40 cm

sinB = 40/50 = 4/5

sinC = 30/50 = 3/5

cosB = 30/50 = 3/5

cosC = 40/50 = 4/5

tgB =40/30 = 4/3

tgC = 30/40 = 3/4

ctgB = 30/40 = 3/4

ctgC = 40/30 = 4/3

Ti-am rezolvat 3 subpuncte. Din exemplele date si formulele scrise am pretentia sa inveti si sa rezolvi tu celelalte 2 subpuncte. Bafta !