Second grade math! ! ! ! ! Pythagorean theorem! ! !

Classification: education/study/examination >> study aid

Problem description:

1. In the known triangle ABC, AB = 7, BC = 6, AC = 4, AD and AE are the height and center line of BC, respectively. Find the length of DC. (There must be a process)

2. The bottom BC of the isosceles triangle ABC has a point D, AD = 13, BD = 8, BC = 15. Find the degree of waist length AC and angle B of isosceles triangle. (process)

It is known that in the Rt triangle ABC, the angle A=90 degrees and the vertical foot of AD is D. If BC= 13 and AB+AC= 17, find the length of AD. (process)

Analysis:

1。 According to the cosine theorem: co * * = (BC 2+AB 2-AC 2)/(2bc * AB) (B is ∠B).

Let DC = x be (6-x)/7 = (6 2+7 2-4 2)/(2 * 6 * 7).

So DC=0.25

2. let AC = X.

Similarly, it can be obtained by cosine theorem.

(x^2+ 15^2-x^2)/(2*x* 15)=(x^2+8^2- 13^2)/(2x*8)

So AC = 15, so it is an equilateral triangle, so ∠ B = 60 degrees.

3. let AC = X and AD = Y, then ab =17-X.

x( 17-x)= 13y

x^2+( 17-x)^2= 13^2

X=5 or 12 and y=60/ 13 can be obtained.