Exact and calculator ratios
Answers are for parents and teachers.
1
Find the exact value of cos 30° tan 60° − sin 30°.
(√3/2)(√3) − 1/2 = 3/2 − 1/2 = 1.
2
A 30°-60°-90° triangle has its short leg 7 cm. Find the other leg and hypotenuse, exactly.
Hypotenuse 14 cm, long leg 7√3 cm.
3
Use a calculator: tan 55° to 4 decimal places, and the angle with cos θ = 0.3 to the nearest degree.
tan 55° ≈ 1.4281; θ ≈ 73°.
4
A 5 m ladder makes 70° with the ground. Find the height it reaches and the foot distance to 2 decimal places.
Height 5 sin 70° ≈ 4.70 m, distance 5 cos 70° ≈ 1.71 m.
5
A pole casts a 9 m shadow when the angle of elevation of the sun is 60°. Find its height exactly.
9 × tan 60° = 9√3 ≈ 15.59 m.