3 years ago

In the figure, angle G measures 117°, angle C measures 22°, and angle E measures 40°.

Mathematics

1 answer:

faltersainse [42]3 years ago

8 0

This is the answer this dumb app made me type 20 characters

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Answer:

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Step-by-step explanation:

Given

$\sin(105^o)$

Required

Solve

Using sine rule, we have:

$\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)$

This gives:

$\sin(105^o) = \sin(60 + 45)$

So, we have:

$\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)$

In radical forms, we have:

$\sin(60 + 45) = \frac{\sqrt 3}{2} * \frac{\sqrt 2}{2} + \frac{\sqrt 2}{2} * \frac{1}{2}$

$\sin(60 + 45) = \frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}$

Take LCM

$\sin(60 + 45) = \frac{\sqrt 6 + \sqrt 2}{4}$

Rewrite as:

$\sin(60 + 45) = \frac{\sqrt 2 + \sqrt 6}{4}$

Hence:

$\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}$

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