Charlene is trying to find the unknown sides of a right triangle with a 30° acute angle, whose hypotenuse measures $12 \sqrt{2}$ $12sqrt2$ . What is Charlene's error?

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Answer 1 · 2018-01-08T13:13:23

Unknown sides are $6 \sqrt{2}, 6 \sqrt{6}$ $6sqrt2, 6sqrt6$

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Three angles of the right triangle are

$A = 30^{0}, B = 60^{0}, C = 90^{0}$ $A = 30^0, B = 60^0, C = 90^0$

Sides will be in the ratio,
$x : x \sqrt{3} : 2 x$ $x : x sqrt3 : 2 x$ as May be seen from the diagram above.

Given hypotenuse $12 \sqrt{2} = 2 x$ $12sqrt2 = 2x$

$x = \frac{12 \sqrt{2}}{2} = 6 \sqrt{2}$ $x = (12sqrt2) / 2 = 6 sqrt2$

Side opposite to $30^{0} = x = 6 \sqrt{2}$ $30^0 = x = 6sqrt2$

Side opposite to $60^{0} = x \sqrt{3} = 6 \sqrt{2} \cdot \sqrt{3} = 6 \sqrt{6}$ $60^0 = x sqrt3 = 6 sqrt2 * sqrt 3 = 6 sqrt6$

Charlene is trying to find the unknown sides of a right triangle with a 30° acute angle, whose hypotenuse measures 12√212sqrt2. What is Charlene's error?