State true or false:
From the top of a tower $h$ meters high, the angles of depression of two objects, which are in line with the foot of the tower are $α$ and $β (β > α),$ then the distance between the two objects is $h (tan β - tan α)$ . (Write 1 for true and 0 for false)

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Solution

Given $h =$ height of the tower
Let,
$k =$ distance between two objects
$l =$ distance between tower and second object

$tan β = \frac{h}{l}, tan α = \frac{h}{l + k}$

$k = h (cot α - cot β)$

Hence the answer is $0$

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State true or false:From the top of a tower h meters high, the angles of depression of two objects, which are in line with the foot of the tower are α and β(β>α), then the distance between the two objects is h(tanβ−tanα). (Write 1 for true and 0 for false)

Given h= height of the towerLet, k= distance between two objectsl= distance between tower and second objecttanβ=hl,tanα=hl+kk=h(cotα−cotβ)Hence the answer is 0

State true or false:
From the top of a tower $h$ meters high, the angles of depression of two objects, which are in line with the foot of the tower are $α$ and $β (β > α),$ then the distance between the two objects is $h (tan β - tan α)$ . (Write 1 for true and 0 for false)

Given $h =$ height of the tower
Let,
$k =$ distance between two objects
$l =$ distance between tower and second object

$tan β = \frac{h}{l}, tan α = \frac{h}{l + k}$

$k = h (cot α - cot β)$

Hence the answer is $0$