Multiple choice

Assertion (A): The shadow of a tower on a level plane is found to be 60 meters longer when sun's altitude is $30^{0}$ than that when it is $45^{0}$ Then the height of the tower is $30$ $(\sqrt{3}+1)$ {meters} Reason (R): The angle of elevation of a top of a tower standing an horizontal plane from a Point $A$ is $\alpha$. After wlaking a distance $d$ meters towards the foot of the tower, the angle elveation is found to be $\beta$ then the height of the tower is $h=\displaystyle \frac{d}{\cot\alpha-\cot\beta}$

  1. Both $A$ and $R$ are ture and $R$ is the correct explanation of $A$
  2. Both $A$ and $R$ are true and  $R$ is not correct explanation of $A$
  3. $A$ is true but $R$ is false
  4. $A$ is false but $R$ is true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The height h = d / (cot(30) - cot(45)) = 60 / (sqrt(3) - 1) = 60(sqrt(3)+1) / 2 = 30(sqrt(3)+1). Both the assertion and the reason are correct, and the reason provides the formula used in the assertion.

AI explanation

Using the formula from the reason, h equals d divided by (cot alpha minus cot beta). Substituting d equals 60, alpha equals 30, and beta equals 45, we get h equals 60 divided by (cot 30 minus cot 45), which is 60 divided by (root 3 minus 1). Rationalizing gives 60 times (root 3 plus 1) divided by 2, which simplifies to 30 times (root 3 plus 1), confirming the assertion is true. The reason gives the correct derivation of this formula, so both are true and the reason correctly explains the assertion.

Keep practicing — related questions