Homework Help: math

Posted by avadhesh on Monday, November 5, 2012 at 5:22am.

in a triangle ABC it is known that AB=AC. Suppose D is the mid point of AC and BD=BC=2. Then the area of the triangle ABC is

math - Reiny, Monday, November 5, 2012 at 7:54am
let AD = DC = x
then AB = 2x
in triangle ABC , angle B = angle C =Ų
in triangle BCD , angle C = angle BDC = Ų
2 angles of one are equal to 2 angles of the other, so they are similar
then:
2/x = 2x/2
2x^2 = 4
x^2=2
x=√2
So triangle ABC has equal sides of 2√2 and a base of 2
which is similar to
√2 : √2 : 1
Using the cosine law we can find angle A
1^2 = √2^2 + √2^2 - 2(√2)(√2)cosA
4cosA = 3
cosA = 3/4
then sinA = √7/4

area ABC = (1/2)(2e√2)(2√2)(√7/4)= √7

check my arithmetic, should have written it out first.

Answer this Question

Related Questions

trig - ABC is an isoscele triangle in which [AB]=[AC]=5cm and [BC]=6cm. ...
Geometry - Can I get help starting this exercise:- Let triangle ABC be such that...
math - Let triangle ABC be a triangle such that angle ACB is 135 degrees. Prove ...
math - Let triangle ABC be a triangle such that angle ACB is 135 degrees. Prove ...
math - in an isosceles triangle ABC ,AB=AC.if AB and AC are produced to D and E ...
math - in an isosceles triangle ABC ,AB=AC.if AB and AC are produced to D and E ...
math - In Triangle ABC, AC = BC and mC = 62°. The longest side of the ...
Math - In Triangle ABC, AC = BC and mC = 62°. The longest side of the ...
Physics - suppose that the separation between speakers A and B is 5.80 m and the...
Geometry- how to write proof - ABC is a right triangle. Angle C is 90 degree. ...

For Further Reading

First Name:
School Subject:
Answer: