Question

What is the distance between B to A Please add the method. The angle is 61 (a bit blurry)

Answer 1

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:

$\sf \tan(\theta)=\dfrac{O}{A}$

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

$\implies \sf \tan(\angle AOH)=\dfrac{8}{19.8}$

$\implies \sf \angle AOH = 22.00069835^{\circ}$

   ∠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:

$\implies \sf \tan(38.99930165^{\circ})=\dfrac{HB}{19.80}$

$\implies \sf HB=19.80 \tan(38.99930165^{\circ})$

$\implies \sf HB=16.03332427$

Therefore:

   AB = AH + BH

⇒ AB = 8 + 16.03332427

         = 24.03 units (nearest hundredth)

Answer 2

• OH=1980

Now

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

AB

• 8+3572
• 3580