Asked by ako
the vertices of the triangle one at (7,4) (1,7) and (-3,-4). find the interior L at the vertex (7,4).
Answers
Answered by
oobleck
It appears that "interior L" means the interior angle at (7,4)
So, call the three vertices A,B,C and you want angle A.
the slope of AB is -1/2
The slope of AC is 4/5
That makes the angles that AB and AC make with the +x-axis
AB: -26.56°
AC: 38.66°
Thus the angle between AB and AC is 26.56+38.66 = 65.22°
or, we can get the lengths of the sides:
AB = √(3^2+6^2) = √45
AC = √(8^2+10^2) = √164
BC = √(11^2+4^2) = √137
Now the law of cosines says that
a^2 = b^2+c^2 - 2bc cosA
137 = 164 + 45 - 2√7380 cosA
cosA = 6/√205
A = 65.22°
So, call the three vertices A,B,C and you want angle A.
the slope of AB is -1/2
The slope of AC is 4/5
That makes the angles that AB and AC make with the +x-axis
AB: -26.56°
AC: 38.66°
Thus the angle between AB and AC is 26.56+38.66 = 65.22°
or, we can get the lengths of the sides:
AB = √(3^2+6^2) = √45
AC = √(8^2+10^2) = √164
BC = √(11^2+4^2) = √137
Now the law of cosines says that
a^2 = b^2+c^2 - 2bc cosA
137 = 164 + 45 - 2√7380 cosA
cosA = 6/√205
A = 65.22°
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.