Question

Fie triunghiul dreptunghic ABC, cu masura unghiului A =90 grade, DC=12 cm si tg C=2/3, unde AD _I_BC, D apartine lui BC.
a) determinati lungimile laturilor triunghiului
b) calculati sin B, cos B, sin C, cos C.

Answer 1

tg C = 2/3 = AD/DC

AD = 8

teorema inaltimi

AD^2 = BD x DC

BD = 16/3

BC = BD + DC = 16/3 + 12

BC = 52/3

teorema catetei

AB^2 = BD x BC = 12 x 52/3

AB = 8/3(√13)

AC^2 = DC x BC = 12 x 52/3

AC = 4√13

sin B = AD/AB

sin B = (3√13)/13

cos B = BD/AB

cos B = (2√13)/13

sin C = AD/DC

sin C = (2√13)/13

cos C = DC/AC

cos C = (3√13)/13