What is Trigonometry?
This article will mntiond these 6 topics, and exapmles of each one.
1 - Finding the area of a triangle
2 - "Law of Cosine" (how and when to use it)
3 - "Law of Sine" (How and when to use it)
4 - Solving an angle with 2 sides have been given
5 - Solving an angle with 1 side and 2 angles have been given
6 - Solving the "6 Trig Functions" with two sides been given
First you have to determine what kind of angle are you solving, there's three kinds of angles
1. Finding the Area of a Triangle
Finding the area only needs two of the sides and them you'd use this formula "Area=ab/2." if it was a right triangle.
Example: Solve the missing side below
Just use the formula "a=ab/2", so it would be a=9*6/2
a=9*6/2 (multiply 9 and 6)
a=54/2 ( divide 54 by 2)
a=27cm
Note: you have to use the same unit of measurement that been used in the tiangle
2. "Law of Cosine" (how and when to use it)
The basic idea of it is if you know two length of wto sides and the angle between them you can solve the whole triangle, and it doesn't have to a right triangle, it could look like this
Keep in mind that in one triangle we will use 6 different symbols, like the one below
Example: Solve the side of ''a"
Now based on the side you trying to solve, Law of Cosine could be used in three different ways
In this case we're using the third one, becuase it has "a=" and we're solving for a, and the the capital letter is always cross from the small the triangle
a²= b² + c²- 2bc cosA (the formula)
a²= 375² + 400² - 2*375*400 cos35 (enetered the numbers)
a²=54879*3867 (the value after entering it the calculater)
(all under the square root )
a=234.3m
3. "Law of Sine" (how and when to use ot)
It will be used when I know the value of an angle and a side that are cross from each other, which will help find other values in the triangle, and that's its equation.
Exapmple: Solve x in the triangle below
(the method that will be used)
(the method after enrering the number instead of values)
(multiplied each sides like the letter X)
(dividing each side by sin15 to make the c by itself)
(the value after dividing sin15)
(your final answer)
You can also find an angle using the Law of Sine
If you're looking to find an angle by using two other sides you will the Law of Sines, which we mentiond before.
Example: Solve for "y" in the triangle below
(use the method of the Law of Sins)
(put number instead of letters)
(multiply each side like the letter X)
(devide each side by 200 to keep sinB by itself)
(The 200 goes away by
deviding it)
You answer
4 - Solving an angle with 2 sides have been given
This kind of examples you'll the "SOH CAH TOA" method
Example: solve the missing angle
First step is to determine which what you have, and in this triangle we have hyotneuse and the opposite, so we got to use c which Cosine
Calculate Adjacent / Hypotenuse = 6,750/8,100 = 0.8333
Step 4 Find the angle from your calculator using cos-1 of 0.8333:
cos a° = 6,750/8,100 = 0.8333
cos-1 of 0.8333 = 33.6° (to 1 decimal place)
5 - Solving an angle with 1 side and 2 angles have been given
All you need to do there is add the angles that you know an then subtract by 180.
Example: Find the missing angle
All you need there is just adding the 35 and the 115 then subtract them by 180
35+115 = 150
180-150 = 30 degree
6 - Solving the "6 Trig Functions" with two sides been given
You can actually solve the whole right triangle by only two sides given.
Example: Solve the right triangle below
In a situation like this you'd want to use the "SOHCAHTOA" method to find the angle A
note: in this example I'm usuig A, but that's not on eof the steps, you can chose any angle
(In the triangle I know the O and the A so we'd use the Tan method)
(To get rid of Tan and keep the A alone you have to use the -1)
Know I know the angle A, and since it's a right triangle there always will be 90 degree angle, so to find the missing angle, we'll just add
10+35=45
!80-45=135
Angle B is 35 degree
Now we're still missing on of the sides which is side c and we can find that by a²+b²=c²
6²+10²=c²
36+100= 136
c=136 degree