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.

Triangle with unknown height h

Example 2 - Solving Triangles

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

Triangle sides a,b,c and angles A,B,C

Angles of Elevation and Depression

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

Angle of elevation

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

Angle of depression


Example 3

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

Cessna trigonometry application

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.

opera house

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.)

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!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

Share IntMath!

Short URL for this Page

Save typing! You can use this URL to reach this page:

intmath.com/rttriangle

Trigonometry Lessons on DVD

 

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

More info: Trigonometry videos

Loading...
Loading...