Question
Find d in the figure. One side of the triangle is 50 the next is 70 what is D.
Answers
GPT-4o mini
To find the length \( d \) in a triangle where two sides are given, you can use the Law of Cosines if you have the included angle, or you can estimate using the triangle inequalities if you know which side \( d \) corresponds with.
If the triangle sides are 50 and 70, and you want \( d \) as the third side, you can determine the possible range for \( d \) as follows:
1. The sum of the lengths of any two sides must be greater than the length of the third side. Therefore:
\( 50 + 70 > d \)
Which gives us:
\[
d < 120
\]
And also:
\( 50 + d > 70 \)
Which gives:
\[
d > 20
\]
And:
\( 70 + d > 50 \)
Which gives:
\[
d > -20 \quad \text{(not applicable since d must be positive)}
\]
So, combining the inequalities, we find that:
\[
20 < d < 120
\]
If you need an exact value for \( d \), more information (like the included angle or whether it's a right triangle or another type) is needed.
If the triangle sides are 50 and 70, and you want \( d \) as the third side, you can determine the possible range for \( d \) as follows:
1. The sum of the lengths of any two sides must be greater than the length of the third side. Therefore:
\( 50 + 70 > d \)
Which gives us:
\[
d < 120
\]
And also:
\( 50 + d > 70 \)
Which gives:
\[
d > 20
\]
And:
\( 70 + d > 50 \)
Which gives:
\[
d > -20 \quad \text{(not applicable since d must be positive)}
\]
So, combining the inequalities, we find that:
\[
20 < d < 120
\]
If you need an exact value for \( d \), more information (like the included angle or whether it's a right triangle or another type) is needed.