Where the length of the ladder is 40ft, the length of the zip line Z is given as: 222.47m. This is solved using Trigonometry.
What is the solution for the above?
First, we start by driving b using the law of sine.
[tex]\frac{b}{sin (15)}$[/tex] = [tex]\frac{40}{sin (90)}$[/tex]
b  = [40 * Sin (15)]/sin (90)
Note that Sin (15) = √3−1)/(2√2
= 0.2588190451
Also note that Sin (90) Â = 1
Hence, b =
b = (0.2588190451 *40)/1
b = 10.35/1
b = 10.35
Next we derive h
Using the same law of sin, we have:
[tex]\frac{b}{sin (15)}$[/tex] = [tex]\frac{h}{sin (75)}$[/tex]
Making h the subject of the formula, we obtain:
h = Â [tex]\frac{b sin(75)}{sin (15)}$[/tex]
Recall that b = 10.35
Thus we have
h = 10.35 * [(√3 + 1) / 2√2] / [(√3−1)/(2√2)]
h  = 10.35 * 3.73
h = 38.62
From the simple trigonometric analysis, we can deduce that:
∠GJH = 90°; and
∠GHJ = 10°
Hence, to get Z
Z/ Sin (90) = h/Sin (10)
making Z the subject of the formula, we have,
Z = h * Sin (90)/ Sin (10)
Z = 38.62 * 1/ 0.1736
Z = 222.47m
Learn more about Trigonometry at:
https://brainly.com/question/24349828
#SPJ1
