The Law of Sines shows the proportional relationship between angles and their opposite sides. It can be used to find side lengths and angle measurements for any triangle.
Example 1:
Given triangle ABC with sides A, B, and C and their respective angles a, b, and c, use the Law of Sines to set up a proportion and solve for x.
sin 71 = x / 12
x = 12 * sin 71 / sin 35
x = 19.8
Example 2:
Given sin A = 20 / x and sin B = 20 / x, solve for x.
sin 13 = 20 / x
x = 20 / sin 13
x = 104.9
Example 3:
Given sin C = x / 14 and sin B = 20 / x, solve for x.
sin 58 = 25 / x
x = 25 / sin 58
x = 29.5
We have practiced using trigonometric ratios to find side lengths and angle measurements in right triangles. The proportional relationship between angles and sides is a fundamental concept in trigonometry.
Example 4:
Given sin A = 29 / x and sin B = 29 / x, solve for x.
sin 77 = 14 / x
x = 14 / sin 77
x = 14.5
Example 5:
Given sin A = x / 18 and sin B = 18 / x, solve for x.
sin 31 = 27 / x
x = 27 / sin 31
x = 57.8
Example 6:
Given sin A = 18 / x and sin B = 18 / x, solve for x.
sin 12 = 24 / x
x = 24 / sin 12
x = 126.6
Trigonometry is a powerful tool for solving problems related to the relationships between angles and sides in triangles. The Law of Sines and the proportional relationship between angles and sides play a crucial role in these calculations.
For further in-depth study, you can refer to Law of Sines notes PDF, Law of Sines notes class 12, Law of Sines notes class 11, Law of Sine problems with solutions, Law of Sine and Cosine PDF, and Finding side lengths and angle measurements PDF.
