# In an isosceles triangle ABC with a base AC = 37 cm, the outer angle at the apex B is 60 degrees.

August 31, 2021 | education

| **In an isosceles triangle ABC with a base AC = 37 cm, the outer angle at the apex B is 60 degrees. Find the distance from vertex c to line AB.**

1. To determine the distance from the vertex C to the lateral side AB of the triangle ABC, draw the perpendicular CH.

2. Angle ABC = 180 ° – 60 ° = 120 °.

3. The angles BAC and ACB are equal as the angles located at the base of an isosceles triangle.

4. Angle BAC = angle ACB = (180 ° – 120 °) / 2 = 30 °.

5. In the ACH triangle, the CH leg is opposite an angle of 30 °, therefore its length is equal to half the length of the hypotenuse:

CH = AC / 2 = 37: 2 = 18.5 cm.

Answer: the distance from the top of C to the lateral side of AB is 18.5 cm.

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