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What are the lengths of side a and b?​

What are the lengths of side a and b?​-example-1

1 Answer

4 votes

Answer:


a =(\sqrt 2)/(2) m


b=(\sqrt 2)/(2) m

Explanation:

Given

The attached triangle

Required

Find a and b

To do this, we make use of the following trigonometry ratio


\sin(\theta) = (Opposite)/(Hypotenuse)

So, we have:


\sin(45) = (a)/(c)


\sin(45) = (b)/(c)

Where


c = 1

So, we have:


\sin(45) = (a)/(1)


\sin(45) = a

Rewrite as:


a =\sin(45)

In radical form:


\sin(45) =(\sqrt 2)/(2)

So:


a =(\sqrt 2)/(2)

Similarly:


\sin(45) = (b)/(c)


\sin(45) = (b)/(1)


\sin(45) = b

Rewrite as:


b = \sin(45)

In radical form:


\sin(45) =(\sqrt 2)/(2)

So:


b=(\sqrt 2)/(2)

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