Question

Two vertical poles of length a and b subtend the same angle 45° at a point on the line joining their feet. Then the square of the distance between their tops is:

Answer 1

Answer:

Two vertical poles of length a and b subtend the same angle 45° at a point on the line joining their feet. Then the square of the distance between their tops is: = 2 (a² + b²)

Step-by-step explanation:

Assumption point lies between the poles

Angle subtended = 45°

Tan45° = Perpendicular / Base

Tan 45° = 1

so perpendicular = base

height of pole = distance of foot of pole from point

Point is at a distance from foot of pole a

& Point is at b distance from pole b

Horizontal Distance between pole = a+b

Vertical distance between top of poles = |a - b|

square of Distance between top poles = ( a + b)² + (|a-b|)²

= a² + b² + 2ab + a² + b² - 2ab

= 2 (a² + b²)