Question

in triangle ABC , angle B = 2x , angle A=3x and angle C=x and side AB =5cm find x and sides AC & BC

Answer 1

Answer:

Step-by-step explanation:

We know by angle sum property of triangle... Sun of all angles of a triangle is 180..

As all the angles are given in the x form.. So

3x+2x+x=180

6x=180

x=180/6=30

We got the value of x =30 so 3x=90,2x=60,x=30

As we got one angle 90 hence we can apply trigonometric function...

Answer 2

$since \: the \: sum \: of \: all \: angles \: in \: a \: triangle \: = 180 \\ \\ therefore \\ \\ 2x + 3x + x = 180 \\ \\ = > 6x = 180 \\ \\ = > x = \frac{180}{6} \\ \\ = > x = 30 \\ \\ therefore \: \\ \\ \\ angle \: \: a = 3 \times x = 3 \times 30 = 90 \\ \\ angle \: b = 2x \times 2 \times 30 = 60 \\ \\ and \: angle \: c = x = 30$


givene side AB=5cm

let side AC = y

and BC = z

now in right angle triangle ABC

$\sin(30) = \frac{5}{z} \\ \\ \frac{1}{2} = \frac{5}{z} \\ \\ = > z = 10 \\ \\ \\ and \: \\ \\ \ \tan(30) = \frac{5}{y} \\ \\ = > \frac{1}{ \sqrt{3} } = \frac{5}{y} \\ \\ = > y = 5 \sqrt{3}$

therefore

AC=
$5 \sqrt{3} cm$

and
BC=10 cm


hope it helps...