Trigonometric ratios of an acute angle
Answers are for parents and teachers.
1
A right triangle has legs 20 and 21 and hypotenuse 29. Find sin, cos and tan of the angle opposite the 20.
sin = 20/29, cos = 21/29, tan = 20/21.
2
For the other acute angle of that triangle find sin and tan. Which ratio equals cos of the first angle?
sin = 21/29 and tan = 21/20. Here sin = 21/29 equals cos of the first angle.
3
sin θ = 7/25. Find cos θ and tan θ.
Adjacent = 24k (25² − 7² = 576). cos θ = 24/25, tan θ = 7/24.
4
cos θ = 3/5 and the hypotenuse is 15 cm. Find the legs and the area.
k = 3: adjacent 9, opposite 12. Area = 9 × 12 ÷ 2 = 54 cm².
5
In △ABC with ∠B = 90° prove that sin A cos C + cos A sin C = 1.
sin A = BC ÷ AC = cos C and cos A = AB ÷ AC = sin C. The sum is (BC² + AB²) ÷ AC² = 1.