Question

Find the sin t as a fraction in simplest terms

Answer 1

We are asked to determine the sinT. To do that let's remember that the function sine is defined as:

`\sin x=(opposite)/(hypotenuse)`

In this case, we have:

`\sin T=(VU)/(VT)`

To determine the value of VU we can use the Pythagorean theorem which in this case would be:

`VT^2=VU^2+TU^2`

Now we solve for VU first by subtracting TU squared from both sides:

`VT^2-TU^2=VU^2`

Now we take the square root to both sides:

`\sqrt[]{VT^2-TU^2^{}}=VU`

Now we plug in the values:

`\sqrt[]{(6)^2+(\sqrt[]{36^{}})^2}=VU`

Solving the squares:

`\sqrt[]{36+36}=VU`

Adding the values:

`\sqrt[]{2(36)}=VU`

Now we separate the square root:

`\sqrt[]{2}\sqrt[]{36}=VU`

Solving the square root:

`6\sqrt[]{2}=VU`

Now we plug in the values in the expression for sinT:

`\sin T=\frac{6\sqrt[]{2}}{6}`

Now we simplify by canceling out the 6:

`\sin T=\sqrt[]{2}`

And thus we obtained the expression for sinT.