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zysi [14]
3 years ago
14

A cone is sliced exactly in half from the vertex to a diameter of the base. What shape is formed?

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
6 0

1. If you're looking for a one-dimensional answer, then the answer would be a triangle (if you're looking at the surface of the cut). The three sides would be the diameter and the slant heights.


2. Again, if you're looking for a one-dimensional answer, the answer would be a rectangle. The four sides would be the diagonals and the heights.

Hope this helps and sorry I couldn't reply sooner!

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It has three supporting details in the order they will be discussed.

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Could someone please help me:) I am stick and I am not sure what to do ​
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Answer:

Part 5.1.1:

\displaystyle \cos 2A = \frac{7}{8}

Part 5.1.2:

\displaystyle \cos A = \frac{\sqrt{15}}{4}

Step-by-step explanation:

We are given that:

\displaystyle \sin 2A = \frac{\sqrt{15}}{8}

Part 5.1.1

Recall that:

\displaystyle \sin^2 \theta + \cos^2 \theta = 1

Let θ = 2<em>A</em>. Hence:

\displaystyle \sin ^2 2A + \cos ^2 2A = 1

Square the original equation:

\displaystyle \sin^2 2A = \frac{15}{64}

Hence:

\displaystyle \left(\frac{15}{64}\right) + \cos ^2 2A = 1

Subtract:

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Take the square root of both sides:

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Since 0° ≤ 2<em>A</em> ≤ 90°, cos(2<em>A</em>) must be positive. Hence:

\displaystyle \cos 2A = \frac{7}{8}

Part 5.1.2

Recall that:

\displaystyle \begin{aligned}  \cos 2\theta &= \cos^2 \theta - \sin^2 \theta \\ &=   1- 2\sin^2\theta \\ &= 2\cos^2\theta - 1\end{aligned}

We can use the third form. Substitute:

\displaystyle \left(\frac{7}{8}\right) = 2\cos^2 A - 1

Solve for cosine:

\displaystyle \begin{aligned} \frac{15}{8} &= 2\cos^2 A\\ \\ \cos^2 A &= \frac{15}{16} \\ \\ \cos A& = \pm\sqrt{\frac{15}{16}} \\ \\ \Rightarrow \cos A &= \frac{\sqrt{15}}{4}\end{aligned}

In conclusion:

\displaystyle \cos A = \frac{\sqrt{15}}{4}

(Note that since 0° ≤ 2<em>A</em> ≤ 90°, 0° ≤ <em>A</em> ≤ 45°. Hence, cos(<em>A</em>) must be positive.)

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