Question

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

Answer 1

Answer:

a. 56 meters

b. 89.7 meters

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

$\frac{AC}{\sin34\degree}=\frac{100}{\sin94\degree}$

Solving for AC gives

$AC=\frac{100\times\sin34\degree}{\sin94\degree}$

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.

$\frac{AC}{\sin32\degree}=\frac{DC}{\sin58\degree}$

Since AC = 56, the above becomes

$\frac{56}{\sin32\degree}=\frac{DC}{\sin58\degree}$

solving for DC gives

$DC=\frac{56}{\sin32\degree}\times\sin58\degree$

which evaluates to give (rounded to the nearest tenth)

$\boxed{DC=89.7}$

Hence, to summerise

a. 56 meters

b. 89.7 meters