Assertion (A): The tangent of 45° is 1. Reason (R): For an angle of 45° in a right triangle, the opposite side

Question

Assertion (A): The tangent of $45 °$ is 1.
Reason (R): For an angle of $45 °$ in a right triangle, the opposite side equals the adjacent side.

Smart Achievers · Accepted Answer

(1)

$I n Δ A B C, r i g h t a n g l e d a t B, l e t ∠ C = 45 ° . \Rightarrow ∠ A = 90 ° - 45 ° = 45 ° \Rightarrow ∠ A = ∠ C \Rightarrow A B = B C = x (s a y) [∵ I n a t r i a n g l e, s i d e s o p p o s i t e t o e q u a l a n g l e s a r e e q u a l] ∴ \tan C = \tan 45 ° = A B / B C \dots (i) [w h e r e A B i s p e r p e n d i c u l a r (o p p o s i t e s i d e) a n d B C i s b a s e (a d j a c e n t s i d e)] \Rightarrow \tan 45 ° = x / x = 1 [∵ A B = B C = x]$

Hence, assertion A is true.

Also reason (R) is true and represents a fact (that for an angle of 45° in a right triangle, the opposite side equals the adjacent side), supporting assertion (A), so it correctly explains the assertion (A).

Solution

Q.
Assertion (A): The tangent of $45 °$ is 1.
Reason (R): For an angle of $45 °$ in a right triangle, the opposite side equals the adjacent side.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

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