Pythagoras and trig ratios; Finding lengths and angles; Two/three-dimensional practical contexts: inclinometers, sun inclination, ladders, cones
Example 1
A right triangle has legs 15m and 20m. Find its hypotenuse.
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Answer: 25
- Pythagoras gives √[(3a)2+(4a)2]=5a.
Example 2
A right triangle has opposite leg 5m and adjacent leg 9m at angle θ. Find θ in degrees. Round to 2 decimal places.
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Answer: 29.05
- tanθ=adjacentopposite. Apply inverse tangent in degrees.
- Rounded result: 29.05.
Example 3
A ladder 10m long makes an angle of 65∘ with level ground. Find its vertical reach. Round to 2 decimal places.
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Answer: 9.06
- The reach is opposite the given angle; use length ×sin65∘.
- Rounded result: 9.06.