Question

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

Answer 1

Answer:

D

Step-by-step explanation:

First, let's find x.

We know that one of the angles is 30. The side opposite to than angle is 11, and x is the adjacent side to it. Therefore, we can use the trig function tangent.

Recall that:

$\tan(x)=opp/adj$

Plug in 30 for the angle, 11 for the opposite, and x for the adjacent. Solve for x by cross-multiplying:

$\tan(30)=11/x\\x\tan(30)=11\\x=11/\tan(30)$

From the unit circle, recall that tan(30) is equal to one over the square root of 3. Thus:

$x=11/(1/\sqrt3)\\x=11\cdot\sqrt3\\x=11\sqrt3$

Now, we can use the Pythagorean Theorem to find y. y is the hypotenuse. Thus:

$c^2=a^2+b^2\\c^2=(11\sqrt3)^2+11^2\\c^2=121(3)+121\\c^2=4(121)\\c^2\sqrt{4(121}=2(11)=22$