The most common use of trigonometry is in right triangles. There are formulas for the sine, cosine and tangent of the acute angle in a right triangle. The shortcut to remember these formulas is known as SOHCAHTOA, which is explained in detail in this lecture. If you're having trouble remembering the word SOHCAHTOA, there's a mnemonic that'll help you remember it more easily. You'll learn how to solve the right triangle using trigonometry. It is important to know that SOHCAHTOA only works in right triangles. For other triangles there are some other rules that can be used, which will be covered in the next lecture.
A right triangle has short sides of length 3 and 4. Find all the angles in the triangle.
A right triangle has one angle measuring 40°
and opposite side of length 6. Find the lengths of all the sides.
The lengths of the two short sides of a right triangle are in a 5:2 ratio. Find all angles of the triangle.
A right triangle has short sides of length 3 and hypotenuse of length 7. Find all the angles in the triangle.
A right triangle has one angle of 65°
and hypotenuse of length 3. Find the lengths of all the sides of the triangle.
Trigonometry in Right Angles
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
My calculator has an arcsine button, it actually writes it as sin-1, which I don't like that notation because makes it seem like a power.0241
In any case, I'm going to use inverse sine of 3/5.0251
There's a very important step here that many students get confused about which is that, if you're looking for an answer in terms of degrees, which in real world measurement, it sometimes easier to use degrees than radians.0257
You have to set your calculator to degree mode.0270
Most calculators have a degree mode and a radian mode.0274
In fact, all calculators that do trigonometric functions have a degree mode and a radian mode.0278
Tan(θ) there, the opposite side is 5, and the adjacent side has length 2.0765
I'm going to find arctan(5/2), θ is arctan(5/2).0772
Remember that you want to have your calculator in degree mode here, because if you have your calculator in radian mode, you'll get an answer in radian which would look very different from any answer in degrees that you were expecting.0783
I calculate arctan(5/2), and it tells me that that is approximately equal to 68.2 degrees.0800