Basic Trigonometric Ratios Question 3

\text{ \small {Note: Figure not drawn to scale.}}

In the figure above, $\cos{(90\degree-x\degree)}=\dfrac{12}{13}$ . What is the value of $\cos{x\degree}$ ?

\dfrac{5}{13}

\dfrac{12}{13}

\dfrac{5}{12}

\dfrac{13}{12}

Approach

An angle defined as $90 \degree - x\degree$ refers to an angle that is complementary to $x\degree$ . We can identify this on the figure as the other acute angle. We can use the cosine ratio accordingly to find a possible length for the adjacent side and hypotenuse.

We can find the 3^rd side using the pythagorean theorem or identifying the 5-12-13 pythagorean triplet. Based on the figure above,

\cos{x\degree}=\frac{\text{adjacent}}{\text{hypotenuse}}

\cos{x\degree}=\frac{5}{13}