Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.
What is the missing length about?
Note that: one has to derive b using the law of sine.
[tex]\frac{b}{sin (15)} = \frac{40}{sin 90}[/tex]
b = [40 x Sin (15)] / sin (90)
So:
Sin (15) = √3−1)/(2√2
= 0.2588190451
Then: Sin (90) = 1
So, b = (0.2588190451 *40)/1
= 10.35/1
= 10.35
So one has to also derive for h
= [tex]\frac{b}{sin (15)} = \frac{h}{sin 75}[/tex]
Note that b = 10.35
Hence : h = 10.35 * [(√3 + 1) / 2√2] / [(√3−1)/(2√2)]
h = 10.35 * 3.73
h = 38.62
Using simple trigonometric analysis, we can say that:
∠ GJH = 90°; and
∠ GHJ = 10°
Therefore, to obtain Z
Z/ Sin (90) = h/Sin (10)
(Then make Z the subject of the formula)
Thus Z = h * Sin (90)/ Sin (10)
Z = 38.62 * 1/ 0.1736
Z = 222.47m
Therefore, Since the length of the ladder is 40ft, the length of the zip line Z will be 222.47m.
Learn more about length from
https://brainly.com/question/23069406
#SPJ1
