Question

What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 5. Base C B is labeled as 6. Segment A D is labeled as x. Segment B D is labeled as 4.2.

Answer 1

x=3.95

Explanation

From the given information we find that the triangle is right angled at C. CB is the base,AC is the height and AB is the hypotenuse.

Given that D is the hypotenuse of the hypotenuse AB.

BC=6

BD=4.2

AD=x

the height and the base of the triangle is given.

Using pythagoras theorem, we can find the hypotenuse AB.

$AB=\sqrt{AC^2+CB^2} \\=\sqrt{5^2+6^2} \\=\sqrt{25+36} \\=\sqrt{61}$

D is the midpoint of AB

therefore AD=AB/2=$\sqrt{61}/2$

=3.905

x=3.905 cm