Solving Right Angled Triangles with Sine and Cosine Ratio

The inverse trigonometric functions sin⁻¹(θ), cos⁻¹(θ), and tan⁻¹(θ) are used to find the unknown measure of an angle of a right triangle when two side lengths are known.

Example 3.3.1:

In ΔABC, find θ and the length of the missing side BC.

To find θ we use the values given in the question. The opposite side and hypotenuse are given so we can use Sin to find θ.

Sin θ = \( \frac{Opposite}{Hypotenuse} \)

Sin θ = \( \frac{AB}{AC} \)

Sin θ = \( \frac{40}{58} \)

Sin θ = \( \frac{20}{29} \)

Sin θ  =  0.6897