Question

Select the true statement about triangle ABC. Need answer asap

Answer 1

Answer:  The correct option is

(B) $\sin C=\cos A.$

Step-by-step explanation:  We are given to select the true statement about the triangle ABC shown in the figure.

From the figure, we note that

triangle ABC is right-angled at angle B, where hypotenuse, AC = 13, BC = 5 and AB = 12.

From the trigonometric ratios, we have

$\sin A=\dfrac{\textup{perpendicular}}{\textup{hypotenuse}}=\dfrac{BC}{AC}=\dfrac{5}{13},\\\\\\\cos A=\dfrac{\textup{base}}{\textup{hypotenuse}}=\dfrac{AB}{AC}=\dfrac{12}{13},\\\\\\\cos B=\dfrac{\textup{base}}{\textup{hypotenuse}}=\dfrac{BC}{AC}=\dfrac{5}{13},\\\\\\\sin C=\dfrac{\textup{perpendicular}}{\textup{hypotenuse}}=\dfrac{AB}{AC}=\dfrac{12}{13},\\\\\\\sin A=\dfrac{\textup{perpendicular}}{\textup{hypotenuse}}=\dfrac{BC}{AC}=\dfrac{5}{13},\\\\\\\tan A=\dfrac{\textup{perpendicular}}{\textup{base}}=\dfrac{BC}{AB}=\dfrac{5}{12}.$

Therefore, we get

$\sin C=\cos A.$

Thus, option (B) is CORRECT.

Answer 2

B. sinC= cosA
Remember SohCahToa.
The sine is equal to opposite/hypotenuse and cosine is equal to adjacent over hypotenuse.
The sine of C is 12/13 and the cosine of A is 12/13.