Answer:
Step-by-step explanation:
Consider triangles BKE and DKA. In this triangles:
as vertical angles;
as alternate interior angles (lines BC and AD are parallel and BC is a transversal);
as alternate interior angles (lines BC and AD are parallel and BE is a transversal).
Thus triangles BKE and DKA are similar by AA theorem. Similar triangles have proportional sides lengths:
Thus, 
Since AD=BC and BC=BE+CE, we have that 4BE=BE+EC, EC=3BE. Hence, the ratio BE to EC is
When a polynomial has four or more terms, the easiest way to factor it is to use <span>grouping</span>
We have the formula tan(a+b)= (tana+tanb): (1-tana x tanb)
And now we have a=80, b=70 and
(tan80+tan70): (1-tan80 x tan70)= tan(80+70)= tan150
If you write 70 for 70°, we have tan150°=1/√3
Merry Christmas
Answer:
c = 175
Step-by-step explanation:
When the height of a right triangle is shown this way (at right angles with the hypotenuse, It can be found by using the way the hypotenuse is broken up. The following proportion works.
576/x = x / 49 Cross multiply
x^2 = 576 * 49
sqrt(x^2) = sqrt(576*49)
x = 24 * 7
x = 168
But that's not what you want (although it is close).
What you want is the hypotenuse to the small lower triangle
c = ?
a = 49
b = 168
c^2 = 49^2 + 168^2
c^2 = 2401 + 28224
c^2 = 30625
c = sqrt(30625)
c = 175
