Question

I need the answers to questions 1&2

Answer 1

Answer:

see explanation

Step-by-step explanation:

(1)

the sine of an angle = $\frac{opposite}{hypotenuse}$

(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 = $\frac{opposite}{adjacent}$

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 = $\sqrt{13}$ ≈ 3.6 ( to nearest tenth )

tanB = $\frac{2}{3}$ ⇒ B = 33.7°

tanA = $\frac{3}{2}$ ⇒ A = 56.3°