Question

Complete the diagram by identifying the missing angles. Use the length of the ladder you chose for the missing length.

Answer 1

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.

$\frac{b}{sin (15)} = \frac{40}{sin 90}$

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

= $\frac{b}{sin (15)} = \frac{h}{sin 75}$

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

brainly.com/question/23069406

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