SESSION 2 (MEASURE OF THE ANGLE IN RADIAN AND DEGREE)¶
MEASURE OF THE ANGLE:¶
There are two ways of measuring the angle:
1) By degree
2) By Radian- CONVERSION BETWEEN DEGREE AND RADIAN:
This following graph will show you how to convert degree to radian and vice versa:
Let's try some examples:
Ex1: Convert $216^{\circ}$ to radian:
With step 3: Start from circle 1 to circle 2, then circle 3. It means
cross-multiplication, then across-division
Ex2: Convert $\frac{8π}{9}$ (rad) to degree:
We use the same rule to solve this problem:
cross-multiplication, then across-divisionNow you are farmiliar with these 3 steps above, just do them quickly as the following solution:
SESSION 1 ( LAW OF SINES & LAW OF COSINES)¶
I. TRIANGLE NOTATIONS:¶
- side c(or AB) is opposite to angle C
- side a(or CB) is opposite to angle A
- side b(or AC) is opposite to angle B
Note: Sometimes other capital letters as D,E,F are assigned as the name of the angle.
II. LAW OF SINES:¶
Question: With the triangle problem, how do you know when to apply Law of Sines?
Answer: It is used when 1 angle and its opposite side are given.
- Example 1:
Notice that: angle A and side a are given.
- Example 2: Find the measure of angle C to the nearest degree
Notice that: angle A and side a are given.
III. LAW OF COSINE¶
Note: When we worked together today, I don't ask you to memorize these three formula. Instead of learning three formula, we only need to learn 1 formula (Less memorized). Remember that we have talked about the improvised formula. Here it is
$(Opp)^2 = (Adj1)^2 + (Adj2)^2 -2(Adj1)(Adj2)cos(angle)$
where:
Opp = Opposite Side
Adj1 = Adjacent Side 1
Adj2 = Adjacent Side 2
Question: With the triangle problem, how do you know when to apply Law of Cosines?
Answer: It is used when
SSS: The case of Side, Side, Side.
SAS: The case of Side, Angle, Side.
Example 1: Find the angle B
Notice that: This is SSS case.(All the sides are given)
Example 2: Find angle B and angle C
Notice that: This is SAS case.(Side Angle Side)
Angle A is between two Adjacent Sides CA and BA.
Question: Why do we need to find side a(or BC) when we are told to find angle B and angle C?
Answer: When side a is calculated, the problem becomes SSS problem. So we apply the law of cosine on angle B and on angleC respectively.(Look at example 1)
IV. NOTE:¶
IV.A) SUM OF ALL ANGLES IN THE TRIANGLE:¶
$\angle{A} + \angle{B} + \angle{C} = 180^{\circ}$
Tip: After you use law of Cosines and law of Sines and you still get stuck with your problem, try using this formula.
IV.B)¶
When you work on your homework, you should not look at the tips of when to apply the law of cosines, the law of sines and the sume of all angles in the triangle. Just try, make mistakes and then draw conclusion about why that formula should not be used in that case. It is the thinking process of how you approach the problem. The Tips are only used when you need to review before the test.
V. LET'S PRACTICE: (SHOW YOUR WORKS)¶
PROBLEM 1
PROBLEM 2
PROBLEM 3
PROBLEM 4
PROBLEM 5
PROBLEM 6
PROBLEM 7
