Q. 4 C5.0( 2 Votes )

In ∆ABC, A is a right angle, then find the values of sin B, cos C and tan B in each of the following :

a. AB = 12, AC = 5, BC = 13

b. AB = 20, AC = 21, BC = 29

c. BC = √2, AB = AC = 1

Answer :

Given that A is a right angle.



(a) AB = 12, AC = 5, BC = 13


To Find : sin B, cos C and tan B


We know that,



Here, θ = B


Side opposite to angle B = AC = 5


Hypotenuse = BC =13


So,


Now, Cos C


We know that,



Here, θ = C


Side adjacent to angle C = AC = 5


Hypotenuse = BC =13


So,


Now, tan B


We know that,



Here, θ = B


The side opposite to angle B = AC = 5


The side adjacent to angle B = AB = 12


So,


(b) AB = 20, AC = 21, BC = 29


To Find: sin B, cos C and tan B


We know that,



Here, θ = B


The side opposite to angle B = AC =21


Hypotenuse = BC =29


So,


Now, Cos C


We know that,



Here, θ = C


Side adjacent to angle C = AC = 21


Hypotenuse = BC = 29


So,


Now, tan B


We know that,



Here, θ = B


The side opposite to angle B = AC = 21


The side adjacent to angle B = AB = 20


So,


(c) BC =√2, AB = AC = 1


To Find: sin B, cos C and tan B


We know that,



Here, θ = B


The side opposite to angle B = AC =1


Hypotenuse = BC =√2


So


Now, Cos C


We know that,



Here, θ = C


Side adjacent to angle C = AC = 1


Hypotenuse = BC = √2


So,


Now, tan B


We know that,



Here, θ = B


The side opposite to angle B = AC = 1


The side adjacent to angle B = AB = 1


So,


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