Assertion (A): If the ratio of the height of a pole and its shadow is \sqrt3:1, then the Sun’s altitude is {30}^\circ. Reason (R): In a right triangle, ta

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Solution

Q.
Assertion (A): If the ratio of the height of a pole and its shadow is $\sqrt{3} : 1$ , then the Sun’s altitude is $30 °$ .

Reason (R): In a right triangle, $t a n θ = \frac{p}{b}$ , where p stands for perpendicular (opposite side to angle θ) and b for base (adjacent side).

1 Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

2 Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

3 Assertion (A) is true but reason (R) is false.

4 Assertion (A) is false but reason (R) is true.

Ans.
(4)

Let AB be the pole and BC be its shadow on the ground.

Here,

$A B : B C = \sqrt{3} : 1 and let ∠ A C B = θ . I n ∆ A B C, w e h a v e : t a n θ = \frac{A B}{B C} = \frac{\sqrt{3}}{1} = \sqrt{3} \Rightarrow t a n θ = t a n 60 ° \Rightarrow θ = 60 ° \Rightarrow {S u n ’ s a l t i t u d e i s 60 \circ .$

Hence, Assertion (A) is false.

Also, the fact given under Reason (R) is the definition of tangent. So, Reason (R) is true.

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