Question

Help with this I don't know how to solve

Answer 1

Answer:

The right answer is the first option, $tg= \frac{\sqrt{105}}{4}$

Step-by-step explanation:

The tg is the ratio of the opposite cathet to the adjacent cathet .

Here b is the opposite cathet, с is the hypotenuse and b is an adjacent cathet.

$tg = \frac{b}{a}$

Let's find b.

$c^2=a^2+b^2\\ b^2=c^2-a^2\\ b^2=22^2-8^2\\ b^2=484-64\\ b^2=420\\ b=\sqrt{420} = \sqrt{2*21*2*5} = 2\sqrt{105}$

Now let's find tgθ.

$tg = \frac{b}{a} \\ tg = \frac{2\sqrt{105}}{8} \\ tg=\frac{\sqrt{105}}{4}$