SOLUTION: Graph the following points on the coordinate plane. Find the measure of ∠ DFE to the nearest hundredth. D (4, 1), E (4, -2), F (-2, -2)

Algebra ->  Pythagorean-theorem -> SOLUTION: Graph the following points on the coordinate plane. Find the measure of ∠ DFE to the nearest hundredth. D (4, 1), E (4, -2), F (-2, -2)      Log On


   

Question 1189696: Graph the following points on the coordinate plane. Find the measure of ∠ DFE to the nearest hundredth.
D (4, 1), E (4, -2), F (-2, -2)
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Graph:

This is a right triangle with legs of
DE = 3
EF = 6
that represent the opposite and adajcent sides for the reference angle DFE (aka angle F)

Use the tangent ratio to connect those two sides
tan(angle) = opposite/adjacent
tan(F) = DE/EF
tan(F) = 3/6
tan(F) = 0.5

Then use the arctangent function, or inverse tangent to get
tan(F) = arctan(0.5)
F = arctan(0.5)
F = 26.56505
F = 26.57

Angle DFE is approximately 26.57 degrees

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

FE is horizontal line y = -2.


Line FD has the slope  m = %281+-+%28-2%29%29%2F%284-%28-2%29%29 = %281%2B2%29%2F%284%2B2%29%29 = 3%2F6 = 1%2F2.


Point  F  is the intersection of these lines  FE and  FD.


Since the slope of line  FD  is  1%2F2,  the angle  DFE  is  arctan%281%2F2%29 = 26.565 degrees.    ANSWER

Solved.