Please help me! I need 3-9 !!

Well, for triangle rectangles, we have the relations:

Cos(A) = (adjacent cathetus)/(hypotenuse)

Sin(A) = (opposite cathetus)/(hypotenuse)

Tan(A) = (opposite cathetus)/(adjacent cathetus)

Where the adjacent cathetus is the cathetus that is adjacent to the angle, the opposite cathetus is the one that is opposite to the angle, and the hypotenuse is the side that is opposite to the 90° angle.

Here we want to solve 3 to 9.

3) We want to find values sin(D) and sin(E) in that triangle.

Remember the above relationship for the sin function, here will have:

sin(D) = 12/15 = 0.8

sin(E) = 9/15 = 0.6

4)

Sin(E) = 12/37 = 0.3243

Sin(D) = 35/37 = 0.9459

5)

Sin(E) = 45/53 = 0.8491

Sin(D) = 28/53 = 0.5283

6)

Remember that: Sin(A) = (opposite cathetus)/(hypotenuse)

In the image, 5 is the adjacent cathetus to the angle A, and the opposite cathetus to angle A is the one in front of it, 12, then the equation should be:

Sin(A) = 12/13

Now we should use the cosine relationship:

Cos(A) = (adjacent cathetus)/(hypotenuse)

7)

Cos(X) = 27/45 = 0.6

Cos(Y) = 36/45 = 0.8

8)

Cos(X) = 15/17 = 0.824

Cos(Y) = 8/17 = 0.4706

9)

Cos(X) = 13/26 = 0.5

Cos(Y) =  (13*√3)/26 = 0.866

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