Question

se considera tringhiul ABCcu masura unghiului A de 90 de grade. Daca AC=24 radical din 2 cm si BC= 8 radical din 30 cm, calculati AB, sin B,cos B, sin C, cos C , tg B , tg C.

Answer 1

[tex] AB^{2} = BC^{2} - AC^{2} = 1920 - 1152\\ \\ AB=16 \sqrt{3} \\ sinC= \frac{AB}{BC} = \frac{16 \sqrt{3} }{8 \sqrt{30} } = \frac{2}{ \sqrt{10} } \\ sinB= \frac{AC}{BC}= \frac{24 \sqrt{2} }{8 \sqrt{30} } = \frac{3}{ \sqrt{15} } \\ cosB=sinC= \frac{2}{ \sqrt{10} } \\ cosC=sinB= \frac{3}{ \sqrt{15} } \\ tgB= \frac{sinB}{cosB} = \frac{3}{ \sqrt{15} } X \frac{ \sqrt{10} }{2} = \frac{3 \sqrt{2} }{2 \sqrt{3} } \\ tgC= \frac{sinC}{cosC} = \frac{2 \sqrt{3} }{3 \sqrt{2} } [/tex]