Five most comprehensive Triangle

laws’ examples

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.

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.

Solution:

Let us find the side a through cosine law formulaSince    (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: 

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°

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.

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°.

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: 

Example 3

= 35°, b = 5, =70°.

Use the Law of Sines to solve the following ASA Triangle.

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.

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.

Example 4

Use the Law of Sine to solve the following SAA Triangle.

= 35°, b = 5, =75°.

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.

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.

Example 5

Use the law of tangents to solve the following triangle:

a is 52, b is 28, and angle = 80 degrees.

Solution:

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

Solution:

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

Solution:

Let us get into the task of determining A + B.

A + B = 180° -A + B = 180 – 80 = 100.Implies:

Solution:

Therefore:

Solve the system of equations for A + B and A – B.

Solution:

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

Solution:

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

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. If still in doubt explore Transtutors…

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