In ΔABC with AB = 5 cm, BC = 12 cm, AC = 13 cm and ∠B = 90°, which of the following is/are not correct?
(A) $\tan C=\frac{12}{13}$
(B) $cosec\, A=\frac{13}{12}$
(C) $\sin B=\frac{5}{13}$
(D) $\tan A=\frac{12}{15}$
(E) $\cos C=\frac{12}{13}$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option 3: (A), (C) and (D) only
In ΔABC with AB = 5 cm, BC = 12 cm, AC = 13 cm and ∠B = 90°
(A) tan C = 12/13:
For angle C: tan C = opposite / adjacent = AB / BC = 5/12
Given 12/13 → Incorrect
(B) cosec A = 13/12
sin A = opposite / hypotenuse = BC / AC = 12/13
cosec A = 13/12 → Correct
(C) sin B = 5/13
B = 90°, so sin B = 1
Given 5/13 is wrong → Incorrect
(D) tan A = 12/15
tan A = opposite / adjacent = BC / AB = 12/5
Given 12/15 = 4/5 → Incorrect
(E) cos C = 12/13
cos C = adjacent / hypotenuse = BC / AC = 12/13 → Correct