Question

What is the value of y?

Enter your answer, as an exact value, in the box.

Answer 1

y = 3.46

Explanation:

In the picture attached there are two triangles smaller and the bigger one.

Both the triangles are right angle triangles.

In both the triangles there is a common side which is hypotenuse of the smaller triangle and the same is base for larger one.

Now from smaller triangle

`sin45=(√(2))/(H)`

`(1)/(√(2))=(√(2))/(h)`

We cross multiply on both sides

h = 2

Now in the bigger triangle

tan60 =
`(y)/(2)`

`√(3)=(y)/(2)`

y = (√3)(2) = 2√3 = 3.46

Answer is y = 3.46

Answer 2

So for the 40-40-90 degree triangle, whenever the two legs are x values, then the hypotenuse is x value times the square root of 2.

--> a changed into a√2
√2 changed in √2 * √2
= 2

So the hypotenuse of the 40-40-90 degree triangle is 2.

Now for the 30-60-90 degree triangle, the smallest leg with the value of x is then changed to the value of x√3 if finding the longer leg.

-> a is changed to a√3
2 is changed into 2√3


So, y is 2√3 or approximately 3.46 units.