MATH SOLVE

10 months ago

Q:
# PLEASE HELP! 100 POINTS!!+ BRAINLIEST!!Two wires help 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.

Accepted Solution

A:

Height of the pole (DC) is 57.2709mStep-by-step explanation:Here, Wire DA and Wire DB supports a pole.Given that Angle, A=54 , B= 72.Also, AB = 23mNow, Taking triangle BCD and Using basic trigonometry Height of pole H = DC[tex]TanB = \frac{DC}{BC}[/tex][tex]BC= \frac{DC}{TanB}[/tex]Now, Taking triangle ACD and Using basic trigonometry[tex]TanA = \frac{DC}{AC}[/tex][tex]AC= \frac{DC}{TanA}[/tex]From figure, we know thatAC = AB + BCAC - BC = AB = 23 Replacing values of AC and BC[tex]\frac{DC}{TanA} - \frac{DC}{TanB}=23\\DC(\frac{1}{TanA}-\frac{1}{TanB})=23[/tex]Now, TanB= Tan72 =3.0776 and TanA = Tan54=1.3763[tex]DC (\frac{1}{1.3763} - \frac{1}{3.0776})_= 23[/tex][tex]DC ( 0.7265-0.3249)= 23[/tex][tex]DC ( 0.4016 )= 23[/tex][tex]DC = 57.2709 [/tex]Thus, Height of thepole is 57.2709m