Respuesta :

Answer:

option 1 is right.

Step-by-step explanation:

Given are five triangles and we have to find the triangle which has angles as 30, 60 and 90

We know that in a right triangle, sin 30 = 1/2

i.e. smaller length is 1/2 of hypotenuse.

Also II leg = hypotenuse sin 30 = [tex]\frac{\sqrt{3} }{2} (hypotenuse)[/tex]

So the sides willbe in the ratio

[tex]1:\sqrt3} :2[/tex] when arranged from smaller to bigger

Compare the given triangle sides with this ratio

First triangle satisfies this with sides 5, 5 rt 3, and 10

Option 1 is right

II triangle satisfies these sides but angle does not appear to be 90 hence false

Option 3 is false because sides are in ratio 1:rt 3:3

Option 4 is wrong because sides are in ratio 1:2rt3:2

Option 5 is wrong because smaller side is not 1/2 of hypotenuse.

Hence only option 1 is right.

The triangle which shows 30°-60°-90° triangle is in option A.

We have to determine

Which triangle is a 30°-60°-90° triangle?

What is a 30°-60°-90° triangle?

In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

The ratio of the length of the triangle is 30°-60°-90° triangle is;

[tex]\rm x:\sqrt{3}x:2x[/tex]

Therefore

The triangle which the ratio of the triangle similar to 30°-60°-90° triangle is;

[tex]\rm x=5\\\\x\sqrt{3} = 5\sqrt{3}\\\\2x= 2(5) =10[/tex]

Hence, the triangle which shows 30°-60°-90° triangle is in option A.

To know more about the 30°-60°-90° triangle click the link given below.

https://brainly.com/question/1674141

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