Refer to the guidelines to solve oblique triangles to decide on the procedure to use to solve ea

Refer to the guidelines to solve oblique triangles to decide...

Key Concepts

ASA/AAS Resolution Strategy

When provided with two angles and one side (either ASA or AAS), the triangle can be solved by first applying the Triangle Angle Sum Property to find the missing angle and then using the Law of Sines to determine the unknown sides. This method is straightforward and provides a systematic approach for handling oblique triangles.

Triangle Angle Sum Property

In any triangle, the sum of the interior angles is always 180 degrees. This property is vital for determining a missing angle when the other two angles are known, which is a common step in solving oblique triangles, especially under the ASA or AAS cases.

Law of Sines

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. This law is essential for solving oblique triangles as it allows for the calculation of unknown sides or angles when given sufficient information such as two angles and one side.

Transcript

00:01 We have 38 number problem in which we have a triangle a b c a b c and small a is equal to 614 .0 this angle a is equal to 35 degree 09 minute angle c is equal to 25 degree and 53 minutes so this is angle angle inside so case one angle angle and side okay now we will be using a plus b plus c equal to 180 degree to find angle b so angle b will be equal to 180 degree minus angle a plus angle c so let just write the values angle b will be equal to 180 degree minus angle a is 35 degree and nine minutes plus 25 degree and 53 minutes this is 180 degree minus 60 degree and 62 minutes now one thing 60 degree 60 minutes equal to 1 degree so 62 minutes will be equal to 1 degree and 2 minutes okay so this will be written as and this can also be written as 179 degree and 60 minutes minus this will become 61 degree 61 degree and 2 minutes so after subtraction we will be getting 58 minutes minutes and 9 minus 8 6 9 minus 1 8 sorry 8 7 minus 6 1 and 1 180 1 18 degree and 58 minutes so this is the value of b is the value of b now we'll be using sign law to calculate all the values of sides so from sign law sign a by a equal to sign b by b equal to sign c by see now if we take these two values we will be getting sign 35 degree or we can say just right first we will be plugging in the values later on sign a by a equal to sign b by b so from here we will be finding out b b will be equal to a into sine b by sine b by sign a now plug in the values a is 614 into sign b we have found out 118 degree 58 minutes 118 degree and 58 minutes divided by sign 35 degree and 9 minutes okay so we need to use calculator let us just find the value sign 118 degree and 58 degrees and 58 minutes divide by sign 35 degree 9 minutes 35 degree and 9 minutes 614 so this will be equal to 933 .0760 so this is the value of b now we need to find the value of c so if we take these two values again these two values so we are taking sign a by a sign a by a equal to sign c by c so c will be equal to c will be equal to a into sign c by sign a now plug in the values a means 614 into sign c means 25 degree 53 minutes divide by sign a means sign 35 degree and so let us write sign of 25 degree 53 minutes divided by a sign of 35 degree and 9 minutes into 614 so this will be 465 .667 so this is the value for c...

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