Question

Given: △AKM, KD ⊥ AM , AK = 6, KM = 10, m∠AKM = 93º Find: KD

Answer 1

Answer:

The measure of the perpendicular KD is 8.72 unit .

Step-by-step explanation:

Given as :

The triangle AKM  , with KD perpendicular to AM

The measure of side AK = 6 unit

The measure of side KM = 10 unit

The ∠ AKM = 93°

Let The measure of side KD = x unit

Now,

∵ KD ⊥ AM , KD divide the angle  ∠ AKM  equally

So,  ∠ AKD =  ∠ $\dfrac{AKM}{2}$

I.e  ∠ AKD =  ∠ $\{93}{2}$

∴  ∠ AKD = 46.5°

Now, Again

Cos Ф =  $\dfrac{AK}{KD}$

I.e Cos 46.5° = $\dfrac{6}{KD}$

I.e 0.688 = $\dfrac{6}{KD}$

∴ KD = $\dfrac{6}{0.688}$

I.e KD = 8.72 unit

Hence The measure of the perpendicular KD is 8.72 unit  Answer