I could really use some help right now. I have been trying to do this for a few hours and still can't seem to find the right answer. If someone could please help me out it would mean a lot to me.

EF is 1.98, AB is 16.23 and HI is 12.22

Step-by-step explanation:

Step 1:

In figure 1, given sin 26° = 0.44 and hypotenuse = 4.5. Use trigonometric ratio sin D to find EF.

sin 26° = EF/DF

⇒ 0.44 = EF/4.5

∴ EF = 0.44 × 4.5 = 1.98

Step 2:

In figure 2, given cos 52° = 0.616 and adjacent side (AC) = 10. Use trigonometric ratio cos A to find hypotenuse (AB).

cos 52° = AC/AB

⇒ 0.616 = 10/AB

∴ AB = 10/0.616 = 16.23

Step 3:

In figure 3, given tan 42° = 0.90 and opposite side (GH) = 11. Use trigonometric ratio tan I to find adjacent side (HI).

tan 42° = GH/HI

⇒ 0.90 = 11/HI

∴ HI = 11/0.90 = 12.22

1) 1.98 units

2) 16.23 units

3) 12.22 units

Step-by-step explanation:

Q1) sin(26) = EF/ FD

0.44 = EF/4.5

EF = 4.5×0.44 = 1.98

Q2) cos(52) = AC/AB

0.616 = 10/AB

AB = 10/0.616

AB = 16.23

Q3) tan(42) = GH/HI

0.9 = 11/HI

HI = 11/0.9

HI = 12.22