Question

Which of the listed values are equal to the sine of C A.)b/a B.)c/a C.)c/b D.)cos B E.)5.Cos C F.)cos (90°-C) G.)cos(90°-B)

Answer 1

Sine of C=?

Among the given options which is the correct one.

Explanation:

Consider a right-angle triangle ABC.

`angle B=90^(0)`

In a right angle triangle, one angle
`90^(o)`.

The sum of all the angles is
`180^(o)`.

`angle A +angle B+angleC=180^(0)angleA+90^(0) +angle C=180^(0)\\angleA+angleC=180^(0) -90^(0) \\angleA+angleC=90^(0) \\angleA=90^(0) -angle C`

Consider the trigonometric ratios and use the traingle ABC.

`SinC=(AB)/(AC)`

`CosA=(AB)/(AC)`

`angleA=angle(90-C)\\Hence,\\SinC=Cos(90-C)`

Answer:

OptionF).
`Sine of C=Cos(90^(0) -C)`