The correct responses found using trigonometric ratios are as follows;
- Brooke's cannot bring the boat back without getting water over her boots.
- The plan will not be approved
- The plane will not disturb
- The company can not use the chimney legally
- The Long company will build the bridge
- The fireman can reach her.
- The lift does not take the skiers up to the bar.
- Eric will be able to see his Dad's plane.
- The 73 m. brace
<h3>How can trigonometric ratios be used to find the right responses?</h3>
1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
- Brooke's cannot bring the boat back without getting water over her boots.
2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
- The plan will not be approved.
3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
- The plane will not disturb.
4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
- The company can not use the chimney legally.
6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
- The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.
7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
- The fireman can reach her.
8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
- The lift does not take the skiers up to the bar.
9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
- Eric will be able to see his Dad's plane.
10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
- The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.
Learn more about trigonometric ratios here:
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, (percent just means "out of 100" so we just divide it by 100) so we can also write: 
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