3 years ago

Triangle sum theorem.

1 answer:

4 0

60 because in triangle ecd d is 35 and c is 43 together they are 78 so the angle that is left is equal to 102 (180-78)
Now in triangle abe the two known angles are 18 and 102 ( vertically opposite angle ) and 18+102 is equal to 120
A= 180-120 =60

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Can someone please give me the answer to the second part of this question?<br> Thank You!

Elena-2011 [213]

Answer:

$\theta=30\textdegree$

Step-by-step explanation:

$(ii)\ \sqrt{3}\tan\ \theta=2\sin \theta\\\\substitute\ \tan\theta=\frac{\sin\theta}{\cos\theta}\\\\\sqrt{3}\frac{\sin\theta}{\cos\theta}=2\sin\theta\\\\Divide\ both\ sides\ by\ \sin\theta.\\\\\sqrt{3}\frac{\sin\theta}{\cos\theta\times \sin\theta}=\frac{2\sin\theta}{\sin\theta}\\\\\frac{\sqrt{3}}{\cos\theta}=\frac{2}{1}\\\\Apply\ cross\ multiplication\\\\2\cos\theta=\sqrt{3}\\\\divide\ both\ sides\ by\ 2\\\\\frac{2\cos\theta}{2}=\frac{\sqrt{3}}{2}\\\\\cos\theta=\frac{\sqrt{3}}{2}\\\\$