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What is the value of x when a triangle has sides in cm of 10 by x by x-2 given that side x-2 is opposite to an angle of 60 degrees?
Wiki User
∙ 7y ago
This can be solved using the cosine rule:
a² = b² + c² - 2bc cos A
where side a is opposite angle A, which is between sides b and c.
From the given information:
angle A = 60°
side a = x - 2
sides b and c are 10 and x (in either order as it doesn't matter).
Then:
(x - 2)² = 10² + x² - 2bc cos 60°
→ x² -4x + 4 = 100 + x² - 2 × 10 × x × ½
→ x² - 4x + 4 = 100 + x² - 10x
→ x² - x² + 10x - 4x = 100 - 4
→ 6x = 96
→ x = 16 cm
Wiki User
∙ 7y ago
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