Question

What is the value of y?

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.

Step-by-step explanation:

Consider ΔABC,

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

$\sin 45^\circ=\dfrac{AB}{AC}\\\\\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{AC}\\\\AC=2\ units$

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

$\tan 60^\circ=\dfrac{DC}{AC}\\\\\sqrt{3}=\dfrac{DC}{2}\\\\DC=y=2\sqrt{3}\ units$

Hence, the value of y is 2√3 units.