Question

Cho ΔABC: góc A = 90^o,AB = 30cm, tan B = \(\dfrac{8}{15}\)

Tính AC, BC

Tính sin B, cos B, cotg B

Answer 1

ta có: tan B=\(\dfrac{8}{15}\)

=>tan B=\(\dfrac{8}{15}=\dfrac{AC}{AB}\)

mà AB=30 cm (gt)

=> AC= 8.30:15=16 cm

xét tam giác ABC vuông tại A (gt) 

=> AC²+AB²=BC²  ( Định lí pytago)

hay 16²+30²=BC²

=>BC=\(\sqrt{16^2+30^2}=34\)

ta có sin B=\(\dfrac{AC}{CB}=\dfrac{16}{34}=\dfrac{8}{17}\)

cos B= \(\dfrac{AB}{BC}=\dfrac{30}{34}=\dfrac{15}{17}\)

cotg B =\(\dfrac{30}{16}=\dfrac{15}{8}\)