Triangle laws made simpler with these 5 comprehensive examples of Triangle law problems by Transtutors

1. Five most
comprehensive Triangle
laws’ examples

2. Struggling to comprehend
“Laws of Triangle”?
All it needs is practise
through through examples!
Find the five most
comprehensive examples of
Laws of Triangle which once
conquered can fetch lifetime
clarity on Triangle laws.

3. Example 1:
Use the Law of Cosines to solve SAS Triangle with the following
specifications:
b=5, =35°, c=4.864.
Two sides of the triangle are given along with the angle between them.

4. Solution:
Let us find the side a through cosine law formula
Since (Law of Cosines)
and
cos(35°)=0.819,
we have
=8.815, a = 2.969.
Next, calculate using Law of Cosines with known
sides a, c and b:

5. Solution:
and =75°. z
Now, let us calculate the third angle of the triangle, having
known other two, and :
= 180° - = 180° - (35°+75°) = 180° - 110° = 70°

6. Example 2:
Use the Law of Cosines to solve SSS Triangle with the following
specifications:
Solve the triangle: a = 2.969, b = 5, c=4.864.

7. Solution:
Let us find the angle using Law of Cosines with known
sides a, b and c through cosine law formula
Since
you have,
Hence =35°.

8. Solution:
and =75°.
Now, we shall calculate the third angle of the triangle,
having known other two, and :
= 180° - = 180° - (35°+75°) = 180° - 110° = 70°.
Next, find the angle in the similar way:

9. Example 3
= 35°, b = 5, =70°.
Use the Law of Sines to solve the following ASA Triangle.

10. Solution:
Let us first find the third angle, .
Since =180°, we have = 180°- =180°-35°-
70°=75°.
Next, we shall calculate side a using Law of Sine with
known side b and angles and :
Let us first find the third angle, .
Since =180°, we have = 180°- =180°-35°-
70°=75°.
Next, we shall calculate side a using Law of Sine with
known side b and angles and :
= b*sin(35°)/sin(75°) =
5*0.574/0.966 = 2.969.

11. Solution:
Now, we will calculate side c using Law of Sine with
known side b and angles and :
=b*sin(70°)/sin(75°) =
5*0.940/0.966 = 4.864.

12. Example 4
Use the Law of Sine to solve the following SAA Triangle.
= 35°, b = 5, =75°.

13. Solution:
Let us find the third angle, .
Since =180°, we have = 180°- =180°-35°-
75°=70°.
Next, we shall calculate side a using Law of Sines with
known side b and angles and :
= b*sin(35°)/sin(75°) =
5*0.574/0.966 = 2.969.

14. Solution:
Let us now calculate side c using Law of Sines with
known side b and angles and :
= b*sin(70°)/sin(75°) =
5*0.940/0.966 = 4.864.

15. Example 5
Use the law of tangents to solve the following triangle:
a is 52, b is 28, and angle = 80 degrees.

16. Solution:
Let us first fill in the values that we know to the tangent
law formula and simplify.

17. Solution:
We will now multiply each side by the denominator on
the right.

18. Solution:
Let us get into the task of determining A + B.
A + B = 180° -
A + B = 180 – 80 = 100.
Implies:

19. Solution:
Therefore:
Solve the system of equations for A + B and A – B.

20. Solution:
Since, A = 69.5,
B = 100 - 69.5 = 30.5.
So, we get
A = 70 and B = 30.

21. Solution:
Now, let us start solving the equation for side c by using
the law of sine.

22. Having understood these five comprehensive examples
covering all the laws of triangle, namely laws of tangent, law
of cosine, and law of sine, you must have generated enough
understanding to be able to solve more triangle law
problems.
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So, are you all set to
practise problems on
triangle laws now?

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