Examples Using Law of Cosines
Example 1: If two sides of the triangle are 12 cm and 16 cm and the angle between them is 30° then find the third side of the triangle.
Solution:
Given,
- b = 12 cm
- c = 16 cm
- ∠A = 30°
Law of Cosines Formula,
a2 = b2 + c2 – 2bc·cosA
⇒ a2 = (12)2 + (16)2 – 2(12)(16)cos30°
⇒ a2 = 144 + 256 – (384)(1/2) = 208
⇒ a = 14.4 cm
Thus, the third side of the triangle is 14.4 cm
Example 2: If two sides of the triangle are 8 cm, 10 cm, and 6 cm then find the angle ‘A’ of the triangle.
Solution:
Given,
- a = 8 cm
- b = 10 cm
- c = 6 cm
Using Cosines Law,
a2 = b2 + c2 – 2bc cos(A)
⇒ cos A = (b2 + c2 – a2)/2bc
Substituting the given value,
cos(A) = (102 + 62 – 82)/(2 × 10 × 6)
⇒ cos(A) = (100 + 36 – 64)/120 = 72/120 = 3/5
⇒ A = cos-1 (3/5)
Law of Cosines
Law of Cosines in Trigonometry is the fundamental law of mathematics used to find the angle of the triangle when all three sides of the triangle are given. This law is also called the Cosine Rule Or the Cosine Formula. If in a triangle the sides are a, b, and c, then law of cosine for angle A is given as:
a2 = b2 + c2 – 2bc cos A
Similarly, all other angles B and C are given. In this article, we will learn about, the Law of Cosines, the Law of Cosines formula, examples, and others in detail.
Table of Content
- What is Law of Cosines?
- Law of Cosines Formula
- Law of Cosines Proof
- How to Find Angle using Law of Cosines
- Sine Formula
- Examples Using Law of Cosines
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