New user? Sign up

Existing user? Log in

Find the value of sin 36 degree geometrically.

Note by Proff Snape 11 months, 4 weeks ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

> This is a quote

This is a quote

# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

Sort by:

Use a regular pentagon!

As you can see, \(\triangle ABP \sim \triangle ABE.\)

Let \(\overline{AB}=1\) for convenience.

Let \(\overline{BE}=x,\) and you see that \(\overline{BP}=x-1.\)

\(x:1=1:x-1;\) solving this yields \(x=\dfrac{1+\sqrt{5}}{2},~\) and therefore,

\(\cos 36^{\circ}=\dfrac{\overline{BE}}{2\overline{AB}}=\dfrac{1+\sqrt{5}}{4}.\)

\(\sin 36^{\circ}=\dfrac{\sqrt{16-(1+\sqrt{5})^2}}{4}=\dfrac{\sqrt{10-2\sqrt{5}}}{4}.\)

Log in to reply

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestUse a regular pentagon!

As you can see, \(\triangle ABP \sim \triangle ABE.\)

Let \(\overline{AB}=1\) for convenience.

Let \(\overline{BE}=x,\) and you see that \(\overline{BP}=x-1.\)

\(x:1=1:x-1;\) solving this yields \(x=\dfrac{1+\sqrt{5}}{2},~\) and therefore,

\(\cos 36^{\circ}=\dfrac{\overline{BE}}{2\overline{AB}}=\dfrac{1+\sqrt{5}}{4}.\)

\(\sin 36^{\circ}=\dfrac{\sqrt{16-(1+\sqrt{5})^2}}{4}=\dfrac{\sqrt{10-2\sqrt{5}}}{4}.\)

Log in to reply