Geometry with right triangles

Question

I have this

How do I find $h$? I know that I must use the cosine of $70$ degrees but I'm not sure how.

Answer 1

If it is a sector, then we know that the length of the hypotenuse of the right triangle is $L$, so we have $$h=L\cos70^\circ.$$

$\qquad\qquad\qquad$

Answer 2

Hint:

If the center of the arc is in the right angle you have: $$ \dfrac{L-h}{h}=\tan 70° $$

that we you can solve for $h$.

If the center of the arc is in the $70°$ angle you have: $$ h=L\cos 70° $$ because the right triangle has hypotenuse $L$ and $h$ is the adiacent side to angle of $70°$.