An acute isosceles triangle has an angle with a measure of 36°, the lengths of the two sides are 1 and 1.618. an angle bisector of the base angle intersects the leg at point p. find the distance between p and the vertex opposite the base.

1 unit

Step-by-step explanation:

See the attached diagram.

ΔABC is an isosceles triangle having ∠A = 36° and base angles ∠B = ∠C = 72°

Now, the bisector of angle B intersects AC at P.

Now, ∠ABP = 36° and ∠A = 36°, hence, ∠APB = 180° - 36° - 36° = 108°

Now, given that AB = AC = 1.618 units  and BC = 1 unit

So, from the property of triangles of ΔABP, we have,  

⇒ units (Approximate) (Answer)

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: