In a triangle, right angled at B, AB = 12 cm and BC = 5 cm. what will be the value of 

(i) sinAcosA

(ii) sinCcosC respectively?

Correct option is C

Given:

In a triangle, right angled at B,

AB = 12 cm

BC = 5 cm.

Concept used:

Pythagoras Theorem rule;

$$H^2 = P^2 + B^2$$ 

$$\begin{aligned}& \operatorname{Sin} \theta=\frac{\text { Height }}{\text { Hypotenuse }} \\& \operatorname{Cos} \theta=\frac{\text { Base }}{\text { Hypotenuse }}\end{aligned}$$​​

Solution:

$$\begin{aligned}&\text { Thus, } \mathrm{AC}=\sqrt{12^2+5^2}=13 \mathrm{~cm}\\&\begin{aligned}& \operatorname{Sin} A=\frac{5}{13} \\& \operatorname{Cos} A=\frac{12}{13}\end{aligned}\end{aligned}$$​​

$$\text { Hence, } \operatorname{Sin} A\cdot \operatorname{Cos} A=\frac{60}{169}$$

$$\begin{aligned}& \operatorname{Sin} C=\frac{12}{13} \\& \operatorname{Cos} C=\frac{5}{13}\end{aligned}$$​​

Hence, Sin C.Cos C = $$\frac{60}{169}$$

Thus, the correct answer is option (c).