Question

In triangle ADC ANGLE ADC=90 ANGLE C=45,AC =8√2 FIND AD

Answer 1

Step-by-step explanation:

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Answer 2

Given,

The two angles in a triangle,

∠ADC = 90°,

∠C = 45°.

The length of AC = $8\sqrt{2}$

To Find,

The length of AD.

Solution,

As per the given information,

AC must be the hypotenuse of the mentioned triangle. (check the diagram attached)

Let the length of AD be $x$. AD will be on the opposite side for ∠C.

Sinθ = $\frac{Opposite side}{Hypotenuse}$

Using the above equation, we can calculate the length of AD.

Since, ∠C = 45°,

⇒Sin45° = $\frac{AD}{8\sqrt{2} }$

⇒ $\frac{1}{\sqrt{2} } = \frac{x}{8\sqrt{2} }$ (∵ Sin45° =$\frac{1}{\sqrt{2} }$)

⇒$x = \frac{8\sqrt{2} }{\sqrt{2} }$

⇒$x = 8$

Henceforth, the length of AD is 8.