Based on the given triangle, the cosine of the 30 degree angle is:

P. S.
It is not 1/3 (third option)

Step-by-step explanation:

Remember SOHCAHTOA

The cosine of an angle in a right triangle is the adjacent sides length divided by the hypotenuses length

In this case, for the angle 30 degrees, the adjacent length is and the hypotenuse's length is 2

So, the cosine of the 30 degree angle is the first option:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it