A 60-footpiece of wire is strung between the top of a tower and the ground, making a 30-60-90 triangle. How far from the center of the base of the tower is the wire attached to the ground? How high is the tower?
2 answers
exactly what is a "center of the base" mean? The base of a tower is a point.
Make a point of memorizing the ratio of sides of the 30-60-90 degree triangle,
the sides are in the ratio of 1 : √3 : 2 in the relation of the angles respectively.
so all you have to do is set up simple ratios, assuming that the base angle in your
diagram is 60°
so base/1 = 60/2
base = 30
height/√3 = 60/2
height = 30√3
notice that 30 : 30√3 : 60 = 1 : √3 : 2
You could of course just take sin30° and cos30°
e.g. cos 30° = height/60
height = 60 cos30
= 60(√3/2) = 30√3 , just as above
the sides are in the ratio of 1 : √3 : 2 in the relation of the angles respectively.
so all you have to do is set up simple ratios, assuming that the base angle in your
diagram is 60°
so base/1 = 60/2
base = 30
height/√3 = 60/2
height = 30√3
notice that 30 : 30√3 : 60 = 1 : √3 : 2
You could of course just take sin30° and cos30°
e.g. cos 30° = height/60
height = 60 cos30
= 60(√3/2) = 30√3 , just as above
1 answer