Question

(e) In triangle ABC tanA=1,tanB=2 then tanC=. ?​

Answer 1

tanC=3 : Answer .

Step-by-step explanation:

tan A = 1

A = tan−11 = 45 deg

tan B = 2

B = tan−1 2 = 63.43 deg

C = 180 - (A + B) = 180 - 108.43 = 81.57 deg

tan C = tan(81.57) = tan(180 - 63.43) = -(tan 180 + tan 63.43)/(1 - tan 180 * tan 63.43)

tan C = -(1 + 2)/(1 - (1 * 2)) = -3/(-1) = 3

Answer 2

The value of tan C is 3.

GIVEN: In triangle ABC, TanA=1, TanB=2
TO FIND: Value of Tan C
SOLUTION:

As we are given in the question,

A triangle ABC With,

Tan A = 1 and Tan B = 2

As we know,

Tan A = 1

A = tan⁻¹ 1

A= 45 deg

Also

Tan B = 2

B = tan⁻¹2

B = 63.43 deg

Now,

Using the angle sum property,

We know,

Angle A + Angle B + Angle C = 180 deg

45 + 63.43 + Angle C = 180 deg

Angle C = 180 - (45 + 63.43)

Angle  C = 180 - 108.43

Angle C = 81.57 deg

Now,

C = 81.57

Taking tan both sides

Tan C = Tan(81.57)

Tan C = Tan(180 - 63.43)

Tan C = -(tan 180 + tan 63.43)/(1 - tan 180 * tan 63.43)

Tan C = -(1 + 2)/(1 - (1 * 2))

Tan C = -3/(-1)

Tan C = 3

Therefore,

The required value of tan C is 3.

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