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)

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w