# The base of an isosceles triangle is 4√3cm, and the height dropped on it is 2 times

October 6, 2021 | education

| **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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