Question

2. The triangles shown are similar. Their similarity coefficient is 1.5. Calculate the lengths of the sides of A1B1C1 and the sizes of the angles.

Answer 1

Given

Two triangles

Find

Length of the side and angle of triangle A1B1C1

Step-by-step explanation

In triangle ABC

angle A = 90 degree

`\begin{gathered} (a)/(\sin A)=(b)/(\sin B) \\ \sin B=(3)/(6)*\sin A \\ \sin B=(1)/(2)*\sin90\degree \\ B=30\degree \end{gathered}`

as we know , sum of all angles of triangle is 180 degree.

so,

`\angle C=180\degree-90\degree-30\degree=60\degree`

now, from

`\Delta A_1B_1C_1`

we have

`\begin{gathered} A_1C_1=(3)/(1.5)=2 \\ B_1C_1=(6)/(1.5)=4 \\ A_1B_1=√(4^2-2^2)=√(16-4)=√(12)=2√(3) \end{gathered}`

Final Answer

Sides are

`\begin{gathered} A_1C_1=2 \\ B_1C_1=4 \\ A_1B_1=2√(3) \end{gathered}`

angles are

`\begin{gathered} \angle A=90\degree \\ \angle B=30\degree \\ \angle C=60\degree \end{gathered}`