Heights and Distances Practice Test 1

Question : 33 of 40

Marks: +1, -0

The angles of elevation of the top of a vertical tower from two points, distant a and b (a > b) fromthe base and in the same straight line with it are complementary. Then the height of the tower is:

$√(ab)$
$√(a^2+b^2)$
$√(a^2-b^2)$
$√{a(a-b)}$

Validate

Solution:

Let CD = h unit be the height of the tower and A and B be the two points on the ground, such that DA = a; DB = b; ∠ DAC = α and ∠ DBC = 90° – α
From right triangle ADC, CD = h = a tan α ...(i)
From right triangle BDC, CD = h = b tan (90° – α) = b cot α ...(ii)
Multiplying equations (i) and (ii), we get

h^2 = a \tan α. b \cot α

Hence,

h =√ {ab}

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