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Which statements are true about angle b in this triangle?​

Which statements are true about angle b in this triangle?​-example-1
User Petrsyn
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1 Answer

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Answer:

b)
\sin(B) = (\sqrt 2)/(2)

e)
\tan(B) = 1

Explanation:

Given

The attached triangle

Required

The true statement about B

The given options show that we determine the correct trigonometry ratio of B.

So, we have:


\cos(B) = (Adjacent)/(Hypotenuse)

This gives:


\cos(B) = (a)/(c)

Where:


a = 3mm\\c = 3\sqrt 2 mm


\cos(B) = (3)/(3\sqrt 2)

3 cancels out


\cos(B) = (1)/(\sqrt 2)

Rationalize


\cos(B) = (1)/(\sqrt 2)* (\sqrt 2)/(\sqrt 2)


\cos(B) = (\sqrt 2)/(\sqrt 2*\sqrt 2)


\cos(B) = (\sqrt 2)/(12)

Also:


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

This gives:


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

Where:


b = 3mm\\c = 3\sqrt 2 mm


\sin(B) = (3)/(3\sqrt 2)

3 cancels out


\sin(B) = (1)/(\sqrt 2)

Rationalize


\sin(B) = (1)/(\sqrt 2)* (\sqrt 2)/(\sqrt 2)


\sin(B) = (\sqrt 2)/(\sqrt 2 * \sqrt 2 )


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

Lastly:


\tan(B) = (\sin(B))/(\cos(B))

This gives:


\tan(B) = (√(2)/2)/(√(2)/2)


\tan(B) = 1

Hence, (b) and (e) are true

User Priyan RockZ
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