4.3 Right Triangle Trig

Remembering SOHCAHTOA Let  be an acute angle of a right triangle. Then…

For a triangle, recall that… 45°

For a triangle, recall that… 30°

Trig Identities… We also have…

The last of the identities are… The Pythagorean Indentities

Now let’s look at some examples 1.If  is an acute angle such that cos  = 0.3, then find the following: a) sin 

b) c) d) e)

Applications First you must make sure your calculator is the proper mode. Evaluate cos 15.3° using your calculator…. You should get .9646 EXAMPLE: If the sun is 30  up from the horizon and shining on a tree forming a 50-foot shadow, how tall is the tree? Start by drawing the picture

Let’s see what this looks like 30° 50 ft h tan 30° = x 50 so x = 50 tan 30° ≈ ft.

Another Example If a rope tied to the top of a flagpole is 35 feet long, then what angle is formed by the rope and the ground when the rope is pulled to the ground, 25 feet from the base of the pole? Again, start by drawing a picture!

Here is the picture! Cool Huh? Black Hawks 35 ft 25 ft °° cos  = 25/35  ≈ ° cos -1 (25/35)