Question

In right ΔABC, right angled at B, AC = 10 cm, and AB = 6 cm. Find the values of sin C, cos C, and tan C

Answer 1

Ans as given above......

Answer 2

Given that,

In a right angled triangle,

• $\rm { AC = 10cm}$
• $\rm {AB = 6cm}$
• $\rm { \angle B = 90° }$

____..

Applying pythagoras property-

$\sf\red { {H}^{2} = {B}^{2} + {P}^{2} }$

$\sf { \leadsto {AC}^{2} = {BC}^{2} + {AB}^{2} }$

$\sf { \leadsto {10cm}^{2} = {BC}^{2} + {6cm}^{2} }$

$\sf { \leadsto {BC}^{2} = {10cm}^{2} - {6cm}^{2} }$

$\sf { \leadsto {BC}^{2} = 100cm - 36cm }$

$\sf { \leadsto {BC}^{2} = 64cm }$

$\sf { \leadsto BC = \sqrt{64cm} =8cm }$

$\rm\red { sin \: C = \dfrac{ side \: opposite \: to \: \angle C }{Hypotenuse} = \dfrac{AB}{AC} = \dfrac{6}{10} }$

$\rm\red { cos \: C = \dfrac{ side \: adjacent \: to \: \angle C }{Hypotenuse} = \dfrac{BC}{AC} = \dfrac{8}{10} }$

$\rm\red { tan \: C = \dfrac{ side \: opposite \: to \: \angle C }{side \: adjacent \: to \: \angle C} = \dfrac{AB}{BC} = \dfrac{6}{8} }$