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
