I do acknowledge those references, sites, and pictures that I use to have this ppt.

2. Law of sine states that a side divided
by the sine of the angle opposite it is
equal to any other side divided by the
sine of the opposite angle.
𝑎
𝑠𝑖𝑛𝐴
=
𝑏
𝑠𝑖𝑛𝐵
=
𝑐
𝑠𝑖𝑛𝑐

3. It can only be used if:
Two angles and a side are known; or
Two sides and an angle opposite one of them are
known.
Law of cosine states that the square of any side of a
triangle is equal to the sum of the squares of the
other two sides minus twice the product of these
sides and the cosine of the angle between them.
𝒄 𝟐
= 𝒂 𝟐
+ 𝒃 𝟐
− 𝟐𝒂𝒃 𝒄𝒐𝒔 𝑪

4. It is only applicable if:
the three sides are known; and
the two sides and its included
angle are known

5. Example 1. Solve for the missing parts
of ∆ABC below. Given: two sides and
an angle opposite of these sides
𝑎 = 10, 𝑐 = 19; ∠𝐶 = 120°

6. Solutions: ∠𝐶 is an obtuse
angle and 𝑐 > 𝑎, thus there
is exactly one solution. Since
a, c and ∠𝐶 are known, we
can use the formula:

8. Using the concept that the sum of the
angles of triangle is 180 𝑜
, we have
∠𝐴 + ∠𝐵 + ∠𝐶 = 180°
27.12° + ∠𝐵 + 120° = 180°
∠𝐵 + 147.12° = 180°
∠𝐵 = 180° − 147.12°
∠𝐵 = 32.88°

9. Following the steps used earlier in solving for
c, we can now solve for b.

10. Given : three sides:
𝑎 = 10; 𝑏 = 15 𝑐 = 20

13. a. What are your thoughts about the
applications of laws of sines and
cosines?

14. b. Are the given illustrations helpful?
How it helps to solve the problem
easier?

15. c. Do you have other way/s to
solve these problems? If so,
share it to the class.

16. Problem #1:
Tony and Obet went to
Tagaytay Oval to fly a kite.
Tony’s kite has 1750𝑓𝑡. of
string at an angle of 75° .
Obet notes that the angle
formed by the kite and the
flier is 102°. How far is Obet
from the kite? Obet from
Tony?

17. Problem #2:
Danna wants to feed her dogs
which are located at different
parts of the house as shown
below. Bantay is 2.5𝑓𝑡 away
from kisig and Kisig is
4.5𝑓𝑡. away from Puti. How
far is Kisig from the food?

19. Answer the following
questions using the
figure below.
1. How far is the
Ranger’s Tower from
the fire?
2. How far is the
Ranger’s Tower from
the Water Tower?

20. The laws of sines states that a side divided by the sine
of the angle opposite it is equal to any other side
divided by the sine of the opposite angle and the laws of
cosines states that the square of the length of one side is
equal to the sum of the squares of the other two sides
minus the product of twice the two sides and the cosine
of the angle between them. These laws are essential in
the solution of oblique triangles. Illustrating a problem
through a diagrams would help connect the problem
with easy understanding.

21. Group Activity
Each group were given an oblique triangle.
Create a situation or a problem where the given oblique
triangle can be applied and write it on the manila paper
given to each group.
The first group who can post their work on the board will
become the first group to present and they will receive an
additional points.
After three minutes each group will demonstrate or act the
situation or problem.
Show the solution to solve the formulated problem.

25. Solve the problem.
Maine’s handheld computer can send and receive e – mails if
it is within 40 𝑚𝑖𝑙𝑒𝑠 of a transmission tower. On a trip Maine
passed the transmission tower on Highway 7 for 32 miles, and
turns 97° onto Coastal road and drive another 19 𝑚𝑖𝑙𝑒𝑠.
a. Is Maine close enough to the transmission tower to be able
to send and receive e – mails? Explain your reasoning.
b. If Maine is within range of the tower, how much farther can
she drive on Coastal road before she is out of range? If she is
out of range and drive back toward Highway 7, how far will
she travels before she is back in range?

27. Ass: Given the figure below answer the following.
a. solve the distance from A to C.
b. how far is B to C?