Question

Assertion (A): In the rectangle PQRS if PS = 4 cm and PR = 8 cm, then 9 = 30°.

Reason (R): tan 45° = 1

Options

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true but R is the incorrect reason for A.

Explanation:

1. Understanding the Triangle:

In rectangle PQRS:

• PS = 4 cm (vertical side)
• PR = 8 cm (diagonal, hypotenuse of right triangle PSR)
• ∠θ is the angle at R between SR and PR.

Using triangle PSR:

• Right triangle with:
  • Opposite side = PS = 4 cm
  • Hypotenuse = PR = 8 cm

Using trigonometry:

`sin theta = "opposite"/"hypotenuse" = 4/8 = 1/2 = theta = 30^(circ)`

So, the Assertion is TRUE.

2. Evaluating the Reason:

“tan 45° = 1” is a true mathematical fact.

Reason is also TRUE.

But does it explain why θ = 30°?

Because tan 45° = 1 has no relevance in calculating θ in this triangle (we used sine, not tangent, and not 45°).