The base AB of isosceles triangle ABC is 6, and the sine of the outer angle at the vertex B is 0.8. Find the side.

Let us mentally lower the height to the base. Since our triangle is isosceles by the condition of the problem, it will be the median.

Let’s find out how long the half of the base will be, it is the leg of the formed triangle:

6: 2 = 3.

According to one basic trigonometric formulas (sin (180 – a) = sin a), the sine of angle B will also be 0.8.

Find out what the cosine will be:

cos B = √ (1 – sin2 B);

cos B = √ (1 – 0.64);

cos B = 0.6.

We then find out the length of the side:

3: 0.6 = 5.

Answer: 5.