Mathematics Topic
Trigonometry: Finding Missing Angles
- Read notes
- Flashcards
- Quiz
- Confident
Study focus - 3 things
- To find missing angles, use inverse sine, inverse cosine, or inverse tangent
- Choose the trig ratio by matching the two known sides
- Calculator use matters: use degree mode and inverse trig correctly
Section 1When finding angles
If two sides are known and an angle is missing, use inverse trigonometry. The calculator buttons may look like sin^-1, cos^-1, and tan^-1. Watch out: sin^-1 is not the same as 1 divided by sine in this topic.
Section 2Choosing the ratio
Label the sides from the angle you want to find. If you know opposite and hypotenuse, use sine. If you know adjacent and hypotenuse, use cosine. If you know opposite and adjacent, use tangent.
Section 3Calculator steps
First form the ratio, then use the inverse trig button. For example, if opposite / hypotenuse = 0.5, then angle = sin^-1(0.5). In degree mode, that gives 30 degrees.
Section 4Checking the answer
Angles in a right triangle must make sense. One angle is 90 degrees, and the other two acute angles add to 90 degrees. If your missing acute angle is 130 degrees, something is wrong.
Examples
A right triangle has opposite side 5 cm and hypotenuse 10 cm. Find the angle.
Use sine: sin angle = 5 / 10 = 0.5. angle = sin^-1(0.5) = 30 degrees.
A ramp at school has rise 1.5 m and horizontal run 4 m. Find the angle it makes with the ground.
Opposite = 1.5 and adjacent = 4, so use tangent. angle = tan^-1(1.5 / 4) = about 20.6 degrees.
Now let's water it
Session runs notes to flashcards to quiz back-to-back.