Question

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Answer 1

Trigonometric ratios are useful in calculating the side lengths of a triangle.

• The length of the zip line is 222.5 ft
• The height where the ladder rests against the tree is 38.6 ft
• The distance between the base of the ladder and that of the tree is 10.4 ft
• The distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft

(a) Length, z

First we calculate (h) using the following sine ratio

$\mathbf{sin(75) = \frac{h}{40}}$

Make h the subject

$\mathbf{h = 40sin(75)}$

Next, we calculate (z) using the following sine ratio

$\mathbf{sin(10)= \frac{h}{z}}$

Make z the subject

$\mathbf{z= \frac{h}{sin(10)}}$

Substitute $\mathbf{h = 40sin(75)}$

$\mathbf{z= \frac{40sin(75)}{sin(10)}}$

$\mathbf{z= 222.5 ft}$

Hence, the length of the zip line is 222.5 ft

(b) The height, h

In (a), we have

$\mathbf{h = 40sin(75)}$

Evaluate

$\mathbf{h = 38.6}$

Hence, the height where the ladder rests against the tree is 38.6 ft

(c) The distance, b

To do this, we make use of the following sine ratio

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

Make b the subject

$\mathbf{b = 40sin(15)}$

$\mathbf{b = 10.4}$

Hence, the distance between the base of the ladder and that of the tree is 10.4 ft

(d) Distance, B

To do this, we make use of the following sine ratio

$\mathbf{sin(80) = \frac{B}{z}}$

Make B the subject

$\mathbf{B = z\ sin(80)}$

Substitute $\mathbf{z= 222.5 ft}$

$\mathbf{B = 222.5\ sin(80)}$

$\mathbf{B = 219.1}$

Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft

Read more about trigonometry ratios at:

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