The length of the small leg of a 30°-60°-90° triangle is 3. What is its perimeter?

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Answer 1 · 2015-11-25T14:23:32

To compute the perimeter of a triangle, you need to know the length of all sides.

Let's call the small leg $a$ $a$ , the big leg $b$ $b$ and the hypotenuse $c$ $c$ .

We already know that $a = 3$ $a = 3$ . Now, let's compute the values of $b$ $b$ and $c$ $c$ .

First, we can compute $b$ $b$ using the $tan$ $tan$ :

$tan = \frac{opposite}{adjacent}$ $tan = ("opposite")/("adjacent")$

$=> tan 60° = b/a = b / 3$

$=> b = tan 60° * 3 = sqrt(3) * 3$

Now, we can compute $c$ either with one of the trigonometric functions or with theorem of Pythagoras:

$a^2 + b^2 = c^2$

$3^2 + (sqrt(3)*3)^2 = c^2$
$<=> 9 + 27 = c^2$

$<=> c = 6$

Now that we have all three sides, we can compute

$P = a + b + c = 3 + 3 sqrt(3) + 6 = 9 + 3 sqrt(3) ~~ 14.196$