Posted by Anonymous on Saturday, March 2, 2013 at 2:02pm.
Let ABC be a right triangle with ACB =90, AC =6 , and BC =2. E is the midpoint of AC , and F is the midpoint of AB . If CF and BE intersect at G , then cos(CGB),
in simplest radical form, is ((k square root w)/f) where k , w , and f are positive integers. Find the value of k+w+ f.
geometry - Steve, Saturday, March 2, 2013 at 7:38pm
Since E and F are midpoints, EF ║ CB, and has length CB/2 = 1
CE = AC/2 = 3
CGB = a
EBC = b
FCB = c
so, intriangle CGB, a+b+c = 180 degrees
cos a = cos *180 - (b+c))
= sinb sinc - cosb cosc
Looking at the right triangles,
EB = √13 and FC = √10, so we have
cos a = 3/√13 * 3/√10 - 2/√13 * 1/√10
= 9/√130 - 2/√130
= 7√130 / 130
k+w+f = 7+130+130 = 267
Answer This Question
More Related Questions
- Maths - In triangle ABC, D is the midpoint of AC and E is the midpoint of AB. BD...
- geometry - I have triangle ABC. Bottom is AC with midpoint F. There is a point ...
- geometry - Triangle ABC, AB=8, BC=10, and AC=12, M is the midpoint of AB, and N ...
- Math - Triangle with vertices: D(-18,12) E(-6,-12) F(12,6) Show that the right ...
- Please help in triangle - ABC is an isosceles triangle with AB=BC and ∠ABC...
- geometry - In the accompanying diagram of triangle ABC side DE is parallel to AC...
- Geometry - Is it possible for AB = 10, BC = 2x + 5 and AC = 5x, given that point...
- geometry - in triangle GHJ, K(2,3) is the midpoint of GH, L(4,1) is the midpoint...
- Geometry - In $\triangle ABC$, we have $AB = AC = 13$ and $BC = 10$. Let $M$ be ...
- mats - in a triangle ABC, D is the midpoint of BC and E is the midpoint of AD. ...