Answer:
24.03 units (nearest hundredth)
Step-by-step explanation:
The distance between B and A is: AB = AH + HB
We have been given AH, so we just need to find the measure of HB.
First, find the angle AOH using tan trig ratio:
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
Given:
- [tex]\theta[/tex] = ∠AOH
- O = AH = 8
- A = OH = 19.80
[tex]\implies \sf \tan(\angle AOH)=\dfrac{8}{19.8}[/tex]
[tex]\implies \sf \angle AOH = 22.00069835^{\circ}[/tex]
∠BOA = ∠BOH + ∠AOH
⇒ ∠BOH = ∠BOA - ∠AOH
⇒ ∠BOH = 61° - 22.00069835°
= 38.99930165°
Now we can find HB by again using the tan trig ratio:
Given:
- [tex]\theta[/tex] = ∠BOH = 38.99930165°
- O = HB
- A = OH = 19.80
Substituting given values:
[tex]\implies \sf \tan(38.99930165^{\circ})=\dfrac{HB}{19.80}[/tex]
[tex]\implies \sf HB=19.80 \tan(38.99930165^{\circ})[/tex]
[tex]\implies \sf HB=16.03332427[/tex]
Therefore:
AB = AH + BH
⇒ AB = 8 + 16.03332427
= 24.03 units (nearest hundredth)
