Which triangle is a 30°-60°-90° triangle?
a. b. c. or d.

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 =

So the sides willbe in the ratio

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 correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.