# Balloon and bridge

From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.

Result

x =  34.097 m

#### Solution:

$h = 92 \ m \ \\ A = 90 - 37 = 53 \ ^\circ \ \\ B = 90 - (30+30/60) = \dfrac{ 119 }{ 2 } = 59.5 \ ^\circ \ \\ \ \\ x_{ 1 } = h \cdot \ \tan( (A \rightarrow rad) = h \cdot \ \tan( (A \cdot \ \dfrac{ \pi }{ 180 } \ ) = 122.088123589 ) \ \\ x_{ 2 } = h \cdot \ \tan( (B \rightarrow rad) = h \cdot \ \tan( (B \cdot \ \dfrac{ \pi }{ 180 } \ ) = 156.185006978 ) \ \\ \ \\ x = |x_{ 1 }-x_{ 2 }| = |122.0881-156.185| \doteq 34.0969 = 34.097 \ \text { m }$

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