Question

Which triangle is a 30°-60°-90° triangle?A. B. C. or D.

Answer 1

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 = $\frac{\sqrt{3} }{2} (hypotenuse)$

So the sides willbe in the ratio

$1:\sqrt3} :2$ 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.

Answer 2

The Very First Triangle is the 30 -60 -90 Degree Triangle