Triangle DEF is an isosceles triangle with DE = FE. If DE = 5 and \(\angle D = 75^\circ\),
a. What is the length of FE? ______________
b. What is the measure of angle F? ___________
c. What is the measure of angle E? ___________
(Note: Please clarify if any additional context or information is needed.)
Answer (3)
First draw a triangle, with D at the top, E at bottom left and F at bottom right.
Dropping the perpendicular bisector from D, to length FE. Angle D/2 = 75/2 = 37.5 degrees. Let the bisector meet FE at G. FE = FG + GE.
Sine 37.5 = (GE)/5 Cross Multiplying. GE = 5Sin37.5. But FE = Twice GE FE = 2*(5Sin37.5) = 10Sin37.5 Evaluate with your calculator. FE = 6.08
b) Measure of Angle F. F is one of the base angles of the isosceles triangle and base angles are equal.
Let Angles of the Isosceles triangle be x, x, 75.
x + x + 75 = 180 Sum of angles in a triangle.
2x + 75 = 180. 2x = 180 -75 2x = 105. Divide by 2. x = 105/2 = 52.5
Therefore angle F = 52.5 degrees.
c) Angle E = Angle F. Angle E = 52.5 degrees.
Cheers.
We are given an isosceles triangle DEF with DE = FE, DE measures 5 units, and angle D measures 75 degrees. An isosceles triangle has at least two sides that are equal in length, so in triangle DEF, since DE = FE, the lengths of DE and FE are the same.
a. Length of FE
Since DE = FE in an isosceles triangle and DE is given as 5 units, the length of FE is also 5 units.
b. Measure of angle F
In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, since angle D is given as 75 degrees, angle F must also measure 75 degrees.
c. Measure of angle E
The sum of the angles in any triangle is 180 degrees. Having already determined that angles D and F each measure 75 degrees, we can find angle E by subtracting the sum of angles D and F from 180 degrees: 180 - 75 - 75 = 30 degrees, which is the measure of angle E.
The length of FE is 5 units, angle F measures 75 degrees, and angle E measures 30 degrees.
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