Question

I need the answers to questions 1&2

Answer 1

see explanation

Explanation:

(1)

the sine of an angle =
`(opposite)/(hypotenuse)`

(a)

here the opposite is 12 and the hypotenuse is 13

12 is the side opposite ∠DEF ← required angle

(b)

the tangent of an angle =
`(opposite)/(adjacent)`

here the opposite is 5 and the adjacent is 12

∠DFE ← required angle

(2)

to calculate AB use Pythagoras' identity in the right triangle

AB² = 2² + 3² = 4 + 9 = 13, hence

AB =
`√(13)` ≈ 3.6 ( to nearest tenth )

tanB =
`(2)/(3)` ⇒ B = 33.7°

tanA =
`(3)/(2)` ⇒ A = 56.3°