Trigo Time
Geometry
Level
2
Find the angle included between the shortest and the longest sides of a triangle whose sides are 4, 6, and 2√7 .
The answer is 60.
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1 solution
Draw a triangle, and name it as ABC, and let the sides, AB = c = 4 , BC = a = 2√7 , AC = b = 6 .
We need to find the angle included to the sides, c and b.
using cosine rule,
a^2 = b^2 + c^2 - 2bc(cos A)
(2√7)^2 = 6^2 + 4^2 - 2(6)(4)(cos A)
28 = 36 + 16 - 48(cos A)
52 - 28 = 48(cos A)
24 = 48(cos A)
1/2 = cos A
60 = A
Therefore, 60 deg. is the answer.