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How do you solve the right triangle given a = 12, c = 6, C = 25°?

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Oct 23, 2015

If $∠ A$ $/_A$ is the right angle
$XXX ∠ B = 65^{\circ}$ $color(white)("XXX")/_B=65^@$ and $b = 6 \sqrt{3}$ $b=6sqrt(3)$
If $∠ B$ $/_B$ is the right angle
$XXX ∠ A = 65^{\circ}$ $color(white)("XXX")/_A=65^@$ and $b = 6 \sqrt{5}$ $b=6sqrt(5)$

Explanation:

The given information allows for two possible configurations (see image below).

Interior angles of a triangle sum to $180^{\circ}$ $180^@$
and since we have a right angle (i.e. $90^{\circ}) and$ $90^@) and$ /_C = 25^@ $t h e t h i r d ∠ μ s t b e$ $the third angle must be$ 65^@#

The length of side $b$ $b$ can be calculated using the Pythagorean Theorem, but its specific value depends upon whether $b$ $b$ is the hypotenuse or an arm of the right angle.
enter image source here

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