Question

The triangle DEF is shown in the diagram.
Find the exact value of x.
​

Answer 1

x = 4

Explanation:

Using cosine triangle formula, we know that;

c² = a² + b² - 2ac(cos C)

From our diagram;

a = 2x

b = x + 1

c = 7

C = 60°

Thus;

7² = (2x)² + (x + 1)² - 2(2x)(x + 1)cos 60

49 = 4x² + (x² + 2x + 1) - (4x² + 4x)(0.5)

49 = 5x² + 2x + 1 - 2x² - 2x

3x² + 1 - 49 = 0

3x² - 48 = 0

3x² = 48

x² = 48/3

x² = 16

x = √16

x = 4