Find the sides of an isosceles triangle ABD with base AD if its height BK is 5, angle A is beta.

According to the properties of an isosceles triangle, we have:

Lateral sides: AB = BD;
At the base angle A = angle D = ც;

ВK – height, bisector and median. Based on this:
ВK – median, AK = KD;
AD = 2 AK;

ВK – height perpendicular to AD;
ВK = 5; Hence:

Triangle ABD rectangular, AB – hypotenuse, AK and BK – legs;

By the definition of trigonometric functions, we can write:

The sin of the angle is the ratio of the opposite leg to the hypotenuse:

Sin A = Sin = BK / AB;

AB = ВK / Sin ც = 5 / Sin ც;

The ratio of the opposite leg to the adjacent leg is tangent.

tg A = tg ც = BK / AK;

AK = BK / tg ც;

AD = 2 * AK = 2 * BK / tg ც = 10 / tg ც;