Trigonometry! #14

Geometry Level 4

If two sides of a triangle and the included angle are given by $a=(1+\sqrt{3})cm$ , $b=2cm$ , $C=60^{\circ}$ , find the other two angles and the third side.

If the other two angles are $x^{\circ}$ and $y^{\circ}$ and the side is $z cm$ , put your answer as $x+y+z^2$ .

This problem is part of the set Trigonometry .

The answer is 126.

1 solution

Andronikus Lumembang
Jan 12, 2015

This is a tricky question, we only need to find the value of $z cm$ and no need to search for exact value of $x$ and $y$ .

We already know that the total of triangle's angle is $180^o$ so :

$x^o + y^o + 60^o = 180^o$

$x^o + y^o = 120^o$

And to find the value of $z cm$ just use the Cosinus's Formula :

$z^2 = (1+ \sqrt{3} )^2 + 2^2 - 2 . (1 + \sqrt{3} ) . 2 . \cos 60^o$

$z^2 = 1 + 2\sqrt{3} + 3 + 4 - 2 - 2\sqrt{3}$

$z^2 = 6$

Thus,

$x + y + z^2 = 120 + 6 = \boxed{126}$

Did the same way.

Niranjan Khanderia - 3 years, 5 months ago

Trigonometry! #14

The answer is 126.

1 solution

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