Question

If cos A = 0.6, then 5 sin A – 3 tan A is equal to

(a) 0 

(b) 1 

(c) 2 

(d) 8

Answer 1

(a) 

cos A = 0.6 = \(\frac{6}{10}=\frac35\)

⇒ cos A = \(\frac{BA}{AC} = \frac35=k\)

⇒ BA = 3k and AC = 5k 

Using Pythagoras’ Theorem 

AC² = BC² + AB² ⇒ (5k)² = BC² + (3k)² 

⇒ BC² = 25k² – 9k² =16k² ⇒ BC = 4k

Now, sin A = \(\frac{BC}{AC} = \frac{4k}{5k}=\frac45,\)

tan A = \(\frac{BC}{AB} = \frac{4k}{3k}=\frac43,\) Now solve.