Question

What is the value of y?

A right triangle has a vertical leg labeled square root of 2 with its opposite angle labeled 45 degrees. A second right triangle has a leg that is the hypotenuse of the first right triangle. At the top of the leg is a 60 degree angle with opposite side labeled y and at the bottom of the leg is the right angle.
Enter your answer, as an exact value, in the box.

Answer 1

The value of y = AC = 2√3

The step by step explanation:

From the figure attached with this answer shows the pictorial representation of the triangles.

To find the value of y

From the figure we can see that,

The triangle ABC is a right angled triangle with angles 45°,45° and 90°

Therefore the sides are in the ratio

AB : BC : AC = √2 : √2 : 2

The triangle ACD is a right angled triangle with angles 45°,45° and 90°

Therefore the sides are in the ratio

AC : CD : AD = 2 : 2√3 : 4

Therefore the value of y = AC = 2√3

Answer 2

Answer:
`y=2√(3)`≈3.46

Explanation:

1. Based on the information given in the problem you can draw the triangles shown in the figures attached, which are not drawn to scale ("x" represents the lenght of the hyteponuse in the first triangle, which is equal to the lenght of a leg in the second triangle).

2. Calculate x using the first triangle:

`sin(45\°)=(√(2))/(x)\\x=(√(2))/(sin(45\°))\\x=2`

3. Now, you can calculate y as following:

`tan(60\°)=(y)/(2)\\y=2*tan(60\°)`

`y=2√(3)`≈3.46