Question

In the right angle ∆ABC, ∠B=900 . If tan C = 3 ,the value of the angle ‘A’ is​

Answer 1

Answer:

30 degree

Step-by-step explanation:

In triangle ABC, angle B=90 degree

tan c=root 3

tan c = opposite/ adjacent

tan c= root3

tan c= 60degree. (because in introduction to trigonometry chapter class 10 table box)

We know that,

angleA + angleB + angle c= 180 degree

angleA + 90degree + 60 degree= 180 degree

angle A + 150 degree = 180 degree

angle A= 180 degree - 150 degree

angle A = 30 degree.

Answer 2

Answer:

The value of Angle A is $A=Tan^{-1}(\frac{1}{3} )$

Step-by-step explanation:

Given that,

In the right angle ∆ABC, ∠B=90* and tan C = 3.We are required to find the value of angle A.

As B=90*,we shall treat AC as an hypotenuse and the sides AB,BC as the opposite and adjacent sides to the angle C respectively.As the value of TanC is 3,We have

$TanC=\frac{AB}{BC} =3$

From the above relation let us assume that-$AB=3K \\BC=K$

Then we obtain the hypotenuse AC from pythagorous theorem as

$AC^{2}=AB^{2}+BC^{2}=(3K)^{2}+K^{2}\\= > AC=\sqrt{10} K$

Now to find angle A,We shall use the trigonometric relations as follows-

$TanA=\frac{BC}{AB} =\frac{K}{3K} =\frac{1}{3} \\A=Tan^{-1}(\frac{1}{3} )$

Hence the value of angle A is found to be $A=Tan^{-1}(\frac{1}{3} )$

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