# 4. The Right Triangle and Applications

Many problems involve right triangles. We often need to use the trigonometric ratios to solve such problems.

### Example 1 - Finding the Height

Find *h*.

### Example 2 - Solving Triangles

Solve the triangle ABC, given that `A = 35°` and `c = 15.67`.

## Angles of Elevation and Depression

In surveying, the **angle of elevation** is
the angle from the horizontal looking **up** to some
object:

The **angle of depression** is the angle from the
horizontal looking **down** to some object:

### Example 3

The angle of elevation of an aeroplane is `23°`. If the aeroplane's altitude is `2500\ "m"`, how far away is it?

### Example 4

You can walk across the Sydney Harbour Bridge and take a photo of the Opera House from about the same height as top of the highest sail.

This photo was taken from a point about `500\ "m"` horizontally from the Opera House and we observe the waterline below the highest sail as having an angle of depression of `8°`. How high above sea level is the highest sail of the Opera House?

Didn't find what you are looking for on this page? Try **search**:

### Online Algebra Solver

This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)

Go to: Online algebra solver

### Ready for a break?

Play a math game.

(Well, not really a math game, but each game was made using math...)

### The IntMath Newsletter

Sign up for the free **IntMath Newsletter**. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

### Share IntMath!

### Trigonometry Lessons on DVD

Easy to understand trigonometry lessons on DVD. See samples before you commit.

More info: Trigonometry videos