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

Answer 1

Unknown sides are #6sqrt2, 6sqrt6#

Three angles of the right triangle are

#A = 30^0, B = 60^0, C = 90^0#

Sides will be in the ratio,
#x : x sqrt3 : 2 x# as May be seen from the diagram above.

Given hypotenuse # 12sqrt2 = 2x#

#x = (12sqrt2) / 2 = 6 sqrt2#

Side opposite to #30^0 = x = 6sqrt2#

Side opposite to #60^0 = x sqrt3 = 6 sqrt2 * sqrt 3 = 6 sqrt6#

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Answer 2

Charlene's error lies in assuming that the side adjacent to the 30° angle is equal to ( 12\sqrt{2} ). However, in a right triangle with a 30° acute angle, the side opposite the 30° angle is usually represented by ( \frac{1}{2} ) times the hypotenuse. Therefore, Charlene should have divided ( 12\sqrt{2} ) by ( 2 ) to find the length of the opposite side. Thus, the correct length of the opposite side would be ( 6\sqrt{2} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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