Select the true statement about triangle ABC.
A. sin C = tan A
B. sin C = cos B
C. sin C = cos A
D. sin C = sin A​

Answer:

C

Step-by-step explanation:

sin C=12/13

cos A=12/13

so sin C=cos A

The trigonometric function gives the ratio of different sides of a right-angle triangle. The correct option is C.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Let's solve the given statement as shown below.

A.)

sin C = tan A

sin C = 12/13

tan A = 5/12

Therefore, the given equation is not true.

B. sin C = cos B

sin C = 12/13

cos B = 5/13

Therefore, the given equation is not true.

C. sin C = cos A

sin C = 12/13

cos A = 12/13

Therefore, the given equation is true.

D. sin C = sin A​

sin C = 12/13

Sin A = 5/13

Therefore, the given equation is not true.

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2
3
4
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X
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3
4
5
-6
-7
-8
-9
-10
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1
2.
3
4
5