What is the length of side x in a 30-60-90 triangle where one side is the square root of 3 and the other side is unknown?

Question

Question

in progress 0

Mathematics Helga 4 years 2021-09-02T07:27:34+00:00 2021-09-02T07:27:34+00:00 1 Answers 5 views 0

Answers ( )

Name*

E-Mail*

Website

Featured image

Browse

Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

Answer*

Tryphena · Answer 1 · 2021-09-02T07:29:12+00:00

Answer:

The length of side x in a 30-60-90 triangle is 2√3.

Step-by-step explanation:

The numbers 30-60-90 are angles, so we need to find the side x of a right triangle with the following information:

θ: is one angle of the right triangle = 30°

α: is the other angle of the right triangle = 60°

a: is one side of the right triangle = √3

b: is the other side of the right triangle =?

x: is the hypotenuse of the right triangle =?

The length of the hypotenuse can be found by Pitagoras:

$x^{2} = a^{2} + b^{2}$ (1)

So, we need to find the side “b”. We can calculate it with the given angles.

From the side “a” we have:

$cos(\alpha) = \frac{a}{x}$

$cos(60) = \frac{\sqrt{3}}{x}$ (2)

From the side “b”:

$sin(\alpha) = \frac{b}{x}$

$sin(60) = \frac{b}{x}$ (3)

Now, we can calculate “b” by dividing equation (3) by equation (2).

$tan(60) = \frac{\frac{b}{x}}{\frac{\sqrt{3}}{x}}$

$b = tan(60)*\sqrt{3} = 3$

Finally, we can find the length of the hypotenuse with equation (1):

$x = \sqrt{a^{2} + b^{2}} = \sqrt{(\sqrt{3})^{2} + (3)^{2}} = 2\sqrt{3}$

Therefore, the length of side x in a 30-60-90 triangle is 2√3.

I hope it helps you!