An observation tower is 75 m high. A support wire is attached to the tower 20 m from the top. If the support wire and the ground form an angle of 46 degrees, what is the length of the support wire, to the nearest thousandth?

76.46 m

Step-by-step explanation:

Height of tower = 75m

Support wire 20 m from top

Angle formed (α) = 46°

Using Pythagoras :

Sinα = opposite / hypotenus

Height used = height of tower - 20 m from top

Height = opposite = (75 - 20)m = 55m

Hypotenus = Length of support wire

Sin 46 = 55m / hypotenus

Hypotenus * sin 46 = 55

0.71934 * hypotenus = 55

Hypotenus = 55/0.71934

Hypotenus = 76.458976

Hence, Lenght of support wire = 76.46 m