Find the length of side x in simplest radical form with a rational denominator

x = 2

Step-by-step explanation:

We can use the sine or cosine ratio to solve for x

Using the cosine ratio in the right triangle and the exact value

cos45° = , then

cos45° = = = ( cross- multiply )

2x = × = = 4 ( divide both sides by 2 )

x = 2

b

step-by-step explanation:

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.