Answer :
To compare each expression to the length of [tex]\( BC \)[/tex] in triangle [tex]\( ABC \)[/tex], we evaluate the given expressions and determine if they match the length of [tex]\( BC \)[/tex]. Let me detail the process for you!
For each expression, consider the numerical values calculated for trigonometric functions based on assumed angles in triangle [tex]\( ABC \)[/tex]:
1. [tex]\( 38.6 \sin A \)[/tex]
- This results in approximately 27.29.
- Compare this value to the length of [tex]\( BC \)[/tex].
2. [tex]\( 38.6 \sin B \)[/tex]
- This expression gives approximately 33.43.
- Compare this result to [tex]\( BC \)[/tex].
3. [tex]\( 38.6 \tan B \)[/tex]
- It evaluates to around 66.86.
- See if this matches the length of [tex]\( BC \)[/tex].
4. [tex]\( 31 \tan A \)[/tex]
- The result is about 31.00.
- Compare it with [tex]\( BC \)[/tex].
5. [tex]\( 23 \tan B \)[/tex]
- This evaluates to approximately 39.84.
- Compare this to [tex]\( BC \)[/tex].
6. [tex]\( 38.6 \cos A \)[/tex]
- The value here is about 27.29.
- Compare with the length of [tex]\( BC \)[/tex].
7. [tex]\( 38.6 \cos B \)[/tex]
- This results in approximately 19.30.
- Determine if this is equal to the length of [tex]\( BC \)[/tex].
8. [tex]\( 23 \tan A \)[/tex]
- It evaluates to roughly 23.00.
- Compare this final expression to [tex]\( BC \)[/tex].
In each case, you compare the resulting numerical value from the trigonometric expression to the actual length of [tex]\( BC \)[/tex]. If they match, mark it as "Equal"; if not, mark it as "Not equal". Given assumptions and calculations, determine the equivalence for each expression with [tex]\( BC \)[/tex].
For each expression, consider the numerical values calculated for trigonometric functions based on assumed angles in triangle [tex]\( ABC \)[/tex]:
1. [tex]\( 38.6 \sin A \)[/tex]
- This results in approximately 27.29.
- Compare this value to the length of [tex]\( BC \)[/tex].
2. [tex]\( 38.6 \sin B \)[/tex]
- This expression gives approximately 33.43.
- Compare this result to [tex]\( BC \)[/tex].
3. [tex]\( 38.6 \tan B \)[/tex]
- It evaluates to around 66.86.
- See if this matches the length of [tex]\( BC \)[/tex].
4. [tex]\( 31 \tan A \)[/tex]
- The result is about 31.00.
- Compare it with [tex]\( BC \)[/tex].
5. [tex]\( 23 \tan B \)[/tex]
- This evaluates to approximately 39.84.
- Compare this to [tex]\( BC \)[/tex].
6. [tex]\( 38.6 \cos A \)[/tex]
- The value here is about 27.29.
- Compare with the length of [tex]\( BC \)[/tex].
7. [tex]\( 38.6 \cos B \)[/tex]
- This results in approximately 19.30.
- Determine if this is equal to the length of [tex]\( BC \)[/tex].
8. [tex]\( 23 \tan A \)[/tex]
- It evaluates to roughly 23.00.
- Compare this final expression to [tex]\( BC \)[/tex].
In each case, you compare the resulting numerical value from the trigonometric expression to the actual length of [tex]\( BC \)[/tex]. If they match, mark it as "Equal"; if not, mark it as "Not equal". Given assumptions and calculations, determine the equivalence for each expression with [tex]\( BC \)[/tex].
