Answer:
(1.) a. 35/37
(2.) d. 12/37
(3.) b 35/12
(4.) d. 12/37
(5.) a. 35/37
(6.) c. 12/35
Explanation:
The sine ratio is sin (θ) = opposite/hypotenuse, the cosine ratio is cos (θ) = adjacent/hypotenuse, and the tangent ratio is tan (θ) = opposite/adjacent.
You can use the mnemonic device SohCahToa to remember the ratios.
There are 6 blanks to fill in so I'll label them 1. through 6. for my explanations:
(1.)
- When A is θ (aka the reference angle), BC is the opposite side and AC is the hypotenuse.
Since BC = 35 and AC = 37, our ratio is sin A = BC / AC = 35/37, or answer a.
(2.)
- When A is θ (aka the reference angle), AB is the adjacent side and AC is the hypotenuse.
Since AB = 12 and AC = 37, our ratio is cos A = AB / AC = 12/37, or answer d.
(3.)
- When A is θ (aka the reference angle), BC is the opposite side and AB is the adjacent side.
Since BC = 35 and AB = 12, our ratio is tan A = BC / AB = 35/12, or answer b.
(4.)
- When C is θ (aka the reference angle), AB is the opposite side and AC is the hypotenuse.
Since AB = 12 and AC = 37, our ratio is sin C = AB / AC = 12/37 or answer d.
(5.)
- When C is θ (aka the reference angle), BC is the adjacent side and AC is the hypotenuse.
Since BC = 35 and AC = 37, our ratio is cos C = BC / AC = 35/37, or answer a.
(6.)
- When C is θ (aka the reference angle), AB is the opposite side and BC is the adjacent side.
Since AB = 12 and BC = 35, our ratio is tan C = AB / BC = 12/35, or answer c.