Question

What is the value of y?

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




Any help is very appreciated! I am completely stuck and have been working on this problem for 45 minutes.

Answer 1

There are two things to know. With a 45-45-90 triangle, the hypotenuse
(longest side) is the shorter side multiplied by √2. So you would multiply √2 * √2 = 2. The hypotenuse of the 45-45-90 triangle. Next we use the second thing to know. In a 30-60-90 triangle. the shorter leg is x, the longer leg is x * √3, and the hypotenuse is 2x. Since y is the longer leg, we use 2x. y = 2(2) = 4. y = 4

Answer 2

Answer: The value of y is 2√3 units.

Explanation:

Consider ΔABC,

We will use " Sine rule " to get the value of AC, which is the base of ΔACD .

`\sin 45^\circ=(AB)/(AC)\\\\(1)/(√(2))=(√(2))/(AC)\\\\AC=2\ units`

Now, Consider ΔACD, we will use "Tangent" to find the value of y.

`\tan 60^\circ=(DC)/(AC)\\\\√(3)=(DC)/(2)\\\\DC=y=2√(3)\ units`

Hence, the value of y is 2√3 units.