If either side of an isosceles triangle measures 24 inches and its base measures 16 inches, then what are its angles?

Answer 1

#A = cos^-1 frac{7}{9}, B = C = pi/2 - A/2#

#24 times 24 times 16 = AB times AC times BC#
we use "cos rule": #16^2 = 24^2 + 24^2 - 2 cdot 24 cdot 24 cdot cos A#
#frac{16^2 - 24^2 - 24^2}{- 2 cdot 24 cdot 24 } = cos A = -frac{(2^4)^2}{2 cdot (2^3)^2 cdot 3^2} + 1 = 1 - 2/9#
#A + B + C = pi ; B = C = x#
#A + 2x = pi Rightarrow x = frac{pi - A}{2}#
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Answer 2

Since an isosceles triangle has two sides of equal length, the angles opposite those sides are also equal. Using the properties of triangles, you can calculate the angles using the law of cosines. Let's denote the length of the equal sides as a (24 inches in this case) and the length of the base as b (16 inches). Then, using the law of cosines:

Cosine of the angle opposite the base (let's call it angle C) can be found using the formula: cos(C) = (b^2 - a^2 - a^2) / (-2 * a * a)

Substitute the values: cos(C) = (16^2 - 24^2 - 24^2) / (-2 * 24 * 24)

Calculate the cosine value: cos(C) ≈ -0.5

Now, find the angle C by taking the arccosine of this value: C ≈ arccos(-0.5) ≈ 120 degrees

Since it's an isosceles triangle, the angles opposite the equal sides are also equal. Thus, each of the other angles (angle A and angle B) will be equal. Therefore, each of these angles is (180 - 120) / 2 = 30 degrees. So, the angles of the isosceles triangle are approximately 30 degrees, 30 degrees, and 120 degrees.

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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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