Respuesta :

Answer:

The correct options are A and E.

Step-by-step explanation:

Triangle 30-60-90 means its a right angles triangle having interior angles 30, 60 and 90.

Let the shorter side be x.

[tex]\cos(60^{\circ})=\frac{AB}{AC}[/tex]

[tex]\frac{1}{2}=\frac{x}{AC}[/tex]

[tex]AC=2x[/tex]

It means hypotenuse is twice long as the shorter leg. Option E is correct.

[tex]\sin(60^{\circ})=\frac{BC}{AC}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{BC}{2x}[/tex]

[tex]\frac{\sqrt{3}}{2}\times 2x=BC[/tex]

[tex]\sqrt{3}x=BC[/tex]

It means the longer leg is √3 times as long as the shorter leg. Option A is correct.

Shorter leg = x

Longer leg =x√3

Hypotenuse = 2x

Therefore options A and E are correct.

Ver imagen DelcieRiveria

The longer leg is √3 times as long as the shorter leg. The hypotenuse is twice as long as the longer leg.

What is the triangle?

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

A triangle with inner angles of 30, 60, and 90 is referred to as a right triangle.

Consider the shorter side to be x. The cos formula is;

[tex]\rm cos \theta = \frac{B}{H} \\\\ cos 60^0 = \frac{AB}{AC}\\\\ \frac{1}{2} = \frac{x}{AC} \\\\AC= 2x[/tex]

Checking for another option;

[tex]\rm sin \ 60^0 = \frac{P}{H} \\\\ \frac{\sqrt{3}}{2} = \frac{BC}{2x} \\\\ \frac{\sqrt 3 }{2} \times 2x = BC \\\\ BC = \sqrt 3 x[/tex]

The statement is got correct from the given option;

A.The longer leg is √3 times as long as the shorter leg.

E.The hypotenuse is twice as long as the longer leg.

Hence, the correct options are A and E.

To learn more about the triangle, refer to:

https://brainly.com/question/2773823

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