The base of an isosceles triangle is 4√3cm, and the height dropped on it is 2 times less than the lateral side. Find the unknown sides and angles of the given triangle.
Let the height be equal to the variable a.
Therefore, the side side can be represented in the form of 2a.
Together with half of the base, they make up a right-angled triangle, so we write down the equation and find out what the side is equal to:
(2a) ^ 2 = a ^ 2 + (4√3: 2) ^ 2;
3a ^ 2 = 12;
a ^ 2 = 4;
a1 = 2;
a2 = -2 (not suitable);
2 * 2 = 4.
Determine what the cosine of the angle at the base is:
2√3: 4 = √3 / 2.
This corresponds to an angle of 30 °.
Then the angle opposite the base is:
180 – 2 * 30 = 120.
Answer: Sides of 4 cm, 2 corners of 30 °, one 120 °.
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