Question

What is the distance between B to A

Please add the method.
The angle is 61 (a bit blurry)

Answer 1

• OH=1980

Now

• tan61=BH/OH
• tan61=BH/1980
• BH=1980tan61
• BH=3572(Rounded)

AB

• 8+3572
• 3580

Answer 2

24.03 units (nearest hundredth)

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:

`\sf \tan(\theta)=(O)/(A)`

where:

• 
  `\theta` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

Given:

• 
  `\theta` = ∠AOH
• O = AH = 8
• A = OH = 19.80

`\implies \sf \tan(\angle AOH)=(8)/(19.8)`

`\implies \sf \angle AOH = 22.00069835^(\circ)`

∠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:

• 
  `\theta` = ∠BOH = 38.99930165°
• O = HB
• A = OH = 19.80

Substituting given values:

`\implies \sf \tan(38.99930165^(\circ))=(HB)/(19.80)`

`\implies \sf HB=19.80 \tan(38.99930165^(\circ))`

`\implies \sf HB=16.03332427`

Therefore:

AB = AH + BH

⇒ AB = 8 + 16.03332427

= 24.03 units (nearest hundredth)