Question #3b066

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Answer 1 · 2018-01-19T15:24:14

Height of the building #color(green)(h = 62.88)# m

Assumption : Angles of elevations #20^0# & #50^0#

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Given :

#/_A = 20^0, /__B = 50^0, AB = 130 m#

To determine the height of the building #color(red)(h)#

Let D be the base of the buil.

#tan 20 = (CD) / (AD) = h / (120 + BD)#

#120 * tan 20 + (BD) * tan (20) = h# Eqn (1)

#tan 50 = (CD) / (BD) = h / (BD)#

#(BD) * tan 50 = h# Eqn (2)#

Substituting value of h in terms of BD in Eqn (1),

# (BD) (tan 50 - tan 20) = 120 * tan 20#

#BD = (120 * tan 20) / (tan 50 - tan 20)#

#BD = 52.7631#

#h = (BD) * tan 50 = 52.7631 * tan 50 ~~ color(green)(62.88)# m

Verification :

#h = (AD) * tan 20 = (120 + 52.7631) * tan 20 ~~ color(green)(62.88)# m