Which relationship in the triangle must be true? A
c
b
C
B
а
sin(B) = sin(A)
sin(B) = cos(90 - B)
COS(B) = sin(180 - B)
cos(B) = (A)

sin(B) = cos(90 - B).

Step-by-step explanation:

To answer this question, you must understand SOH CAH TOA.

SOH = Sine; Opposite divided by Hypotenuse

CAH = Cosine; Adjacent divided by Hypotenuse

TOA = Tangent; Opposite divided by Adjacent

I roughly drew a triangle for reference. Let's say we have a 3-4-5 triangle.

As you can see, sin(b) does not equal sin(a). To get the sine of an angle, you would do opposite over hypotenuse. For angle B, that would be 3/5, while for angle A, that would be 4/5.

As stated above, sin(B) is 3/5. Now, if you did cos(90 - B), it would be the same thing as cos(A). This is because the triangle is a right triangle. Since a triangle has 180 degrees, and one angle is a right triangle, the other two angles will add up to be 90 degrees. So, 90 - B = A. cos(A) is the same thing as adjacent over hypotenuse, which is 3/5. So, sin(B) = cos(90 - B) must be true.

Let's just check the others to make sure they are false.

cos(B) = 4/5.

sin(180 - B) is basically the same thing as sin(A + C), which is definitely NOT 4/5.

cos(B) = 4/5, which is NOT the same as A.

So, your answer is sin(B) = cos(90 - B).

Hope this helps!

the answer is n

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.