100 +
two wires support a pole. the wire at point a forms an angle of 54° with the ground and the wire at point b forms an angle of 72° with the ground. the distance between the wires on the ground is 23 m. find the height of the pole to the nearest tenth of a meter.

Height of the pole (DC) is 57.2709m

Step-by-step explanation:

Here, Wire DA and Wire DB supports a pole.

Given that Angle, A=54 , B= 72.

Also, AB = 23m

Now, Taking triangle BCD and Using basic trigonometry

Height of pole H = DC

Now, Taking triangle ACD and Using basic trigonometry

From figure, we know that

AC = AB + BC

AC - BC = AB = 23

Replacing values of AC and BC

Now, TanB= Tan72 =3.0776 and TanA = Tan54=1.3763

Thus, Height of thepole is 57.2709m

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)