A high school question - The calculation of triangles is in the triangle ABC, BC = 2. Point D is on AC, and AD = 1 and CD = 2. If ∠BDC = 2∠A, calculate the size of sinA value.

A high school question - Calculation of triangles

is on triangle ABC, BC = 2. Point D is on AC, and AD = 1 and CD = 2.

If ∠BDC = 2∠A, calculate the size of sinA value. ,

Solution: Here are two methods to calculate

Method 1: Use half-angle formula ,

According to ∠BDC = ∠A + ∠BDA

and ∠BDC = 2∠A

So ∠BDA = ∠A

So ∠BDA = ∠A

So ∠A

So ∠DBA is an isosceles triangle,

So , so BD=AD=1,

And in the triangle BDC, according to the known BC=DC=2, it is an isosceles triangle,

is over C to make BD, and the hang foot is F, Then FD=BD/2=1/2

Therefore,

According to the half-angle formula:

Solution 2: Use the formula of triple angle

This formula can be used to derive the formula of 2 times angles, and directly give the result here

Use sine theorem in triangle ABC ,

Let ∠A=α. Since the triangle BCD is an isosceles triangle (derived from the known side length), ∠CBA=3∠A=3α,

applies the sine theorem to the triangle ABC, and AC=3

AC/sin∠CBA=BC/sinA

that is, 3/sin3α=2/sinα

brings the three-angle formula, and you can find