Trigo Shortest Distance
In this video, you will learn how to find the shortest distance from a point to a line using the area of a triangle in trigonometry. You will see how forming a triangle allows you to apply trigonometric concepts to calculate the perpendicular distance accurately and effectively.
Related Lessons:
Shortest Distance From Point To Line
To calculate the shortest distance from a point to a line, we make use of the area of triangle trigo formula. Let say we have a triangle ABC with side of length a, b and c. If ∠CAB=θ and the shortest distance from point A to the line BC is d:
\[
\begin{align*}
area\mathrm{\ of\ } △&=\frac{1}{2}×c×d\\
\frac{1}{2}×𝑎×𝑏×sin𝜃&=\frac{1}{2}×c×d\\
d&=\frac{𝑎×𝑏×sin𝜃}{c}\\
\end{align*}
\]
Example
In the diagram, ∠ABC=90°, ∠CAD=60°, ∠ACD=40°, AB=5cm and AC=9cm. Calculate
- the length of BC
- ∠BAC
- the length of AD
- the shortest distance from C to AD