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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
<u>(a) Length, z</u>
First we calculate (h) using the following sine ratio
Make h the subject
Next, we calculate (z) using the following sine ratio
Make z the subject
Substitute
Hence, the length of the zip line is 222.5 ft
<u>(b) The height, h</u>
In (a), we have
Evaluate
Hence, the height where the ladder rests against the tree is 38.6 ft
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<u>(c) The distance, b</u>
To do this, we make use of the following sine ratio
Make b the subject
Hence, the distance between the base of the ladder and that of the tree is 10.4 ft
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<u>(d) Distance, B</u>
To do this, we make use of the following sine ratio
Make B the subject
Substitute
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
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