Question

What is the ratio of the sides of triangle ABYNEED HELP ASAP

Answer 1

GIVEN:

We are given two right triangles as indicated and these are;

$\begin{gathered} \Delta ABY\text{ } \\ \\ \Delta YXZ \end{gathered}$

Required;

To find the ratio of the sides of the triangle ABY.

Step-by-step solution;

We shall take into consideration the values of the special angles as shown in the right triangles and these are as follows;

$\begin{gathered} Angle\text{ }30\degree: \\ \\ sin30\degree=\frac{1}{2} \\ \\ cos30\degree=\frac{\sqrt{3}}{2} \\ \\ tan30\degree=\frac{1}{\sqrt{3}} \end{gathered}$$\begin{gathered} Angle\text{ }60\degree: \\ \\ sin60\degree=\frac{\sqrt{3}}{2} \\ \\ cos60\degree=\frac{1}{2} \\ \\ tan60\degree=\sqrt{3} \end{gathered}$$\begin{gathered} Angle\text{ }45\degree: \\ \\ sin45\degree=\frac{\sqrt{2}}{2} \\ \\ cos45\degree=\frac{\sqrt{2}}{2} \\ \\ tan45\degree=1 \end{gathered}$

Observe carefully that the line AB is also the OPPOSITE of angle 30 degrees. This means line AB can also take on the value 1

That is,

$AB=1$

Then the line BY is the hypotenuse of triangle ABY and its length is 2.

That is;

$BY=2$

Line YA is the ADJACENT of triangle ABY and its length is √2.

That is;

$YA=\sqrt{2}$

These can be better illustrated as follows;

Therefore, from the side lengths derived as shown above, the ratio of the sides of triangle ABY is as follows;

$1:2:\sqrt{2}$

ANSWER:

The fourth option is the correct answer.