Question

ADC=90⁰ ,C=45 ,and AC =8 find AD​

Answer 1

Step-by-step explanation:

ADC=90⁰, C=45 and AC=8 find AD

AD² = AC²+DC²

AD² = 8²+45² = 64+2025 = 2089

AD =√2089 = 45.7

Answer 2

So, In this Right Angled Triangle,

Right Angled at "D",

C=$45^{o}$

AC=8 (Let's say "cm")

First, we need to find the the third angle (∠A) i.e.

45+90+A=$180^{o}$(Angle Sum Property of a Triangle)

135+A=180

180-135=y

∠A=$45^{o}$

∴∠A=∠C=$45^{o}$

Which Means, the sides opp. to them will also be equal!

i.e. CD=DA

Now, By Pythagoras Theorem:

We know that Hypotenuse's square = sum of squares of other 2 sides

So, $8^{2}$ = $AD^{2}$+$CD^{2}$

But, AD=CD (Proved above)

Therefore, $8^{2}$ = $AD^{2}$+$AD^{2}$

64=2$AD^{2}$

$\frac{64}2}$=$AD^{2}$

$\sqrt{32}$=AD

AD=5.65

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