two equal sides of an isosceles triangle are (3x-1) units and (2x +2) units. The third side is 2x units. Find the measure of each angle
Answers
STEP 1: Solve x:
Given that the two sides are equal
3x - 1 = 2x + 2
3x - 2x = 2 + 1
x = 3
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STEP 2: Find the length of the 3 sides:
Side 1 = 3x - 1 = 3(3) - 1 = 8 units
Side 2 = 2x + 2 = 2(3) + 2 = 8 units
Side 3 = 2x = 2(3) = 6 units
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STEP 4: Find each of the angles:
Find the angle in-between the two lines with equal length:
Cosine rule : a² = b² + c² - 2bc Cos A
6² = 8² + 8² - 2 (8) (8) CosA
36 = 64 + 64 - 128CosA
128cosA = 128 - 26
128cosA = 102
cosA = 51/64
A = cos⁻¹ (51/64)
A = 37.2°
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The other 2 equal angles = 180 - 37.2 = 142.8
1 angle = 142.8 ÷ 2 =71.4
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Answer: The angles are 71.4°, 71.4° and 37.2°