Evaluate without a calculator: tan (sin-1 ((√ 7)/7)

let's say for a second that that angle is θ, so we can say that

let us notice something, the opposite side is positive, that means either the I or II Quadrant, however the sin⁻¹ function has a range constrained to π/2 to -π/2, which excludes the II Quadrant, so that means that θ must be on the I Quadrant, where the adjacent side or cosine or "x" is positive too.

now, let's use the pythagorean theorem to get the adjacent side for θ

i think it is everything has to equal 180 so, if i correct 4=c. 6=d. 8=a. 7=b. and the last question would be c. because they are parallel lines and they are congruent.

step-by-step explanation:

the reason everything has to equal to 180 is because that is how it works. i'm guessing that is its rule. 4 and 8 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 6 and 7 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 60+60 is 180. so, now you have your answer