Assertion (A): If the length of shadow of a tower is equal to its height, then the Sun’s altitude is {45}^\circ.

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Q.
Assertion (A): If the length of shadow of a tower is equal to its height, then the Sun’s altitude is $45 ° .$

Reason (R): $s i n 45 ° = 1 .$

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.
(3)

Let AB be the tower and BC be its shadow on the ground such that $A B = B C = x$

$I n ∆ A B C, w e h a v e : t a n ∠ C = \frac{Perpendicular}{Base} = \frac{A B}{B C} \Rightarrow t a n ∠ C = \frac{x}{x} = 1 = t a n 45 ° \Rightarrow {S u n ’ s a l t i t u d e i s 45 \circ . H e n c e, A s s e r t i o n (A) i s t r u e . B u t R e a s o n (R) i s f a l s e b e c a u s e : s i n 45 ° = \frac{1}{\sqrt{2}} \neq 1$

Solution

Q.
Assertion (A): If the length of shadow of a tower is equal to its height, then the Sun’s altitude is $45 ° .$

Reason (R): $s i n 45 ° = 1 .$

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.

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Solution

Q. Assertion (A): If the length of shadow of a tower is equal to its height, then the Sun’s altitude is 45°. Reason (R): sin 45° = 1.

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. (3) Let AB be the tower and BC be its shadow on the ground such that AB=BC=x In∆ABC,wehave:tan ∠C=PerpendicularBase=ABBC⇒tan ∠C=xx=1=tan45°⇒{Sun’s altitude is 45∘.Hence, Assertion (A) is true. But Reason (R) is false because:sin45°=12≠1

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Q.
Assertion (A): If the length of shadow of a tower is equal to its height, then the Sun’s altitude is $45 ° .$

Reason (R): $s i n 45 ° = 1 .$