1(viii)
Assertion (A): If the length of shadow of a person is equal to his height, then the angle of elevation of the sun is 45°.
Statement 2: For any right-angled triangle, tan θ = $\frac{\text{Perpendicular}}{\text{Base}}$
- (a)(A) is true, (R) is false.
- (b)(A) is false, (R) is true.
- (c)Both (A) and (R) are true, and (R) is the correct reason for (A).
- (d)Both (A) and (R) are true, and (R) is the incorrect reason for (A).
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Let AB = Height of person and BC = Length of shadow.
∠ACB = θ (Angle of elevation of sun)
Given,
Length of shadow of a person (BC) = height of person (AB)
⇒ tan θ = $\frac{\text{Perpendicular}}{\text{Base}}$
⇒ tan θ = $\frac{\text{AB}}{\text{BC}}$
⇒ tan θ = $\frac{\text{AB}}{\text{AB}}$
⇒ tan θ = 1
⇒ tan θ = tan 45°
⇒ θ = 45°.
∴ Both (A) and (R) are true, and (R) is the correct reason for (A).
Hence, option 3 is the correct option.