Use of Surds in Trigonometric Ratios

Topic Content:

Recall the following trigonometric ratios of special angles: 

Example 1.5.1:

The diagonal of a rectangle is 4 cm long and makes an angle of 60° with one side. What is the length, in cm, of the longest side of the rectangle?

Solution:

Sin 60° = \(\frac {opp}{hyp} = \frac{x}{4}\)

= \(\frac {\sqrt{3}}{2} = \frac{x}{4}\)

\( \scriptsize 2x = 4 \sqrt {3}\)

\( \therefore \scriptsize x = \normalsize \frac{4 \sqrt {3}}{2} \\ \scriptsize = 2 \sqrt {3}\)

Example 1.5.2:

From the top of a vertical mast 150 m