Question

Hello, I need help solving question 22 a & b please, thanks

Answer 1

a. 56 meters

b. 89.7 meters

Step-by-step explanation:

Part A.

The distance from A to the foot of the pole is the segment AC.

First, we find the measure of angle ∠ BCA.

Since ∠ BCA is part of a triangle,

`34\degree+52\degree+∠BCA=180^o`

Solving for ∠ BCA gives

`∠BCA=94^o`

Next, we use the law of sines, which in our case says

`(AC)/(\sin34\degree)=(100)/(\sin94\degree)`

Solving for AC gives

`AC=(100*\sin34\degree)/(\sin94\degree)`

which we evaluate to get (rounded to the nearest whole number.

`\boxed{AC=56.}`

Part B.

The height of the pole is the length DC.

Let us first find the measure of the angel ∠ADC.

Since ∠ADC is the interior angle of a triangle,

`58\degree+90\degree+∠ADC=180\degree`

solving for ∠ADC gives

`∠ADC=32^o`

Now we use the law of sines again.

`(AC)/(\sin32\degree)=(DC)/(\sin58\degree)`

Since AC = 56, the above becomes

`(56)/(\sin32\degree)=(DC)/(\sin58\degree)`

solving for DC gives

`DC=(56)/(\sin32\degree)*\sin58\degree`

which evaluates to give (rounded to the nearest tenth)

`\boxed{DC=89.7}`

Hence, to summerise

a. 56 meters

b. 89.7 meters