Question

PLEASE HELP! 100 POINTS!!+ BRAINLIEST!!

Answer 1

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

$TanB = \frac{DC}{BC}$

$BC= \frac{DC}{TanB}$

Now, Taking triangle ACD and Using basic trigonometry

$TanA = \frac{DC}{AC}$

$AC= \frac{DC}{TanA}$

From figure, we know that

AC = AB + BC

AC - BC = AB = 23

Replacing values of AC and BC

$\frac{DC}{TanA} - \frac{DC}{TanB}=23\\DC(\frac{1}{TanA}-\frac{1}{TanB})=23$

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

$DC (\frac{1}{1.3763} - \frac{1}{3.0776})_= 23$

$DC ( 0.7265-0.3249)= 23$

$DC ( 0.4016 )= 23$

$DC = 57.2709$

Thus, Height of thepole is 57.2709m