If the angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it are complementary, then the height of the tower is

Question

If the angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it are complementary, then the height of the tower is (A) a b (B) √a b (C) (a/b) (D) √(a/b)

Tardigrade Admin · Accepted Answer

In triangle ABC tan θ=(h/a).....(i) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/4d6d4728eba442343bd6db7b3ed1bc44-.png" /> tan (90-θ)=( h / b ) In triangle ABC tan (90-θ)=( h / a ) By equation (i) and (ii) tan θ ⋅ cot θ =( h / a ) ⋅ ( h / b ) ⇒ h 2= ab ⇒ h =√ ab

Q. If the angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it are complementary, then the height of the tower is

$ab$

$ab$

$\frac{a}{b}$

$\frac{a}{b}$

In $△ A BC$
$tan θ = \frac{h}{a}$ .....(i)

$tan (90 - θ) = \frac{h}{b}$
In $△ A BC$
$tan (90 - θ) = \frac{h}{a}$
By equation (i) and (ii)
$tan θ \cdot cot θ = \frac{h}{a} \cdot \frac{h}{b}$
$\Rightarrow h^{2} = ab \Rightarrow h = ab$

Q. If the angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it are complementary, then the height of the tower is

ab

ab​

ba​

ba​​

In △ABC tanθ=ah​.....(i) tan(90−θ)=bh​ In △ABC tan(90−θ)=ah​ By equation (i) and (ii) tanθ⋅cotθ=ah​⋅bh​ ⇒h2=ab⇒h=ab​

Q. If the angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it are complementary, then the height of the tower is

$ab$

$ab$

$\frac{a}{b}$

$\frac{a}{b}$

In $△ A BC$
$tan θ = \frac{h}{a}$ .....(i)

$tan (90 - θ) = \frac{h}{b}$
In $△ A BC$
$tan (90 - θ) = \frac{h}{a}$
By equation (i) and (ii)
$tan θ \cdot cot θ = \frac{h}{a} \cdot \frac{h}{b}$
$\Rightarrow h^{2} = ab \Rightarrow h = ab$