Examples on Law of Sine and Cosine
Example 1: Find the missing side of a triangle having its two sides 12 cm and 8 cm with the angle between them measuring 60°.
Solution:
Given,
- b = 12 cm
- c = 8 cm
- Angle between b and c (A) = 60°
Using Law of Cosine Formula
a2 = b2 + c2 – 2bc. cosA
=>a2 = (12)2 + (8)2 – 2(12)(8)cos60°
=>a2 = 144 + 64 – 192×0.5
=>a2 = 208-96
=>a2 = 112
=>a = 10.58cm
Thus, remaining side of the triangle is 10.58 cm
Example 2: Find the missing side of a triangle having its two sides 25 cm and 10 cm with the angle between them measuring 30°.
Solution:
Given,
- b = 25 cm
- c = 10 cm
- Angle between b and c (A) = 30°
Using Law of Cosine Formula
a2 = b2 + c2 – 2bc. cosA
=>a2 = (25)2 + (10)2 – 2(25)(10)cos30°
=>a2 = 625 + 100 – 500 × 0.86
=>a2 = 725 – 430
=>a2 = 295
=>a = 17.17 cm
Thus, remaining side of the triangle is 17.17 cm
Example 3: Find the missing side of a triangle having other two sides 21 cm and 14 cm with the angle between them equal to 45°.
Solution:
Given
- b = 21 cm
- c = 14 cm
- Angle between b and c (A) = 45°
Using Law of Cosine Formula
a2 = b2 + c2 – 2bc. cosA
=>a2 = (21)2 + (14)2 – 2(21)(14)cos45°
=>a2=441 + 196 – 588 × .707
=>a2 = 637 – 415.7
=>a2 = 221.3
=>a = 14.87 cm
Thus, remaining side of the triangle is 14.87 cm
Law of Sine and Cosine
Law of Sine and Cosine are the basic laws or rules used in trigonometry that are used to give the relation between sides and angles of the triangle. In this article, we will learn about the Law of Sine (Sine Rule), Sine Rule Formula, Law of Cosine (Cosine Rule), Cosine Rule Formula, and others in detail.
Table of Content
- What is Law of Sines(Sine Rule)?
- What is Law of Cosine(Cosine Rule)?
- Law of Sine and Cosine Formula
- Examples Using Law of Sine and Cosine
- Practice Questions on Law of Sine and Cosines