
How to find the missing length of an obtuse triangle if two sides have a length of 10 one of the angles is 120 degrees?
Answer
466.8k+ views
Hint: In this question we need to find the length of side of an obtuse triangle, for this we need to know the other two sides and the opposite angle, we will need to use the version of the Cosine Rule where is the subject of the formula, which is given by,
, Side is the one we are trying to find. Sides and are the other two sides, and angle is the angle opposite side , by substituting the given values in the formula we will get the required length of the side.
Complete step by step answer:
Given two sides have a length of 10 one of the angles is 120 degrees,
So, here angle = , and
Length of the two sides which are equal = 10,
So, we need to find the length of the other side, we will use the version of the Cosine Rule where is the subject of the formula, which is given by,
, Side is the one we are trying to find. Sides and are the other two sides, and angle is the angle opposite side .
So, here , and , and we need to find the side , by substituting the values in the formula we get,
,
Now substituting the values we get,
,
We know that , by substituting the values we get,
,
Now simplifying we get,
,
Now simplifying we get,
,
Again simplifying we get,
,
Now again simplifying we get,
,
Now taking out the square root we get,
,
Now further simplifying we get,
,
So, the length of the side is .
Note: The Cosine Rule is used in the following cases:
1. Given two sides and an included angle (SAS)
2. Given three sides (SSS)
The Cosine Rule states that the square of the length of any side of a triangle equals the sum of the squares of the length of the other sides minus twice their product multiplied by the cosine of their included angle. Some important formulas related to Cosine rule are given below:
,
,
.
Complete step by step answer:
Given two sides have a length of 10 one of the angles is 120 degrees,
So, here angle =
Length of the two sides which are equal = 10,
So, we need to find the length of the other side, we will use the version of the Cosine Rule where
So, here
Now substituting the values we get,
We know that
Now simplifying we get,
Now simplifying we get,
Again simplifying we get,
Now again simplifying we get,
Now taking out the square root we get,
Now further simplifying we get,
So, the length of the side is
Note: The Cosine Rule is used in the following cases:
1. Given two sides and an included angle (SAS)
2. Given three sides (SSS)
The Cosine Rule states that the square of the length of any side of a triangle equals the sum of the squares of the length of the other sides minus twice their product multiplied by the cosine of their included angle. Some important formulas related to Cosine rule are given below:
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