Triangle DEF is an isosceles triangle with DE = FE. If DE = 5 and �ÚD = 75 degrees:
what is the length of FE, the measure of angle F, and the measure of angle E?
E
D ∆ F
You could drop a perpendicular DP, where P is on EF, bisecting angle D and creating a right angled-triangle.
then sin37.5° = EP/5
then EF = 2EP = 2(5sin37.5°) = appr 6.0876
angle E = 90-37.5 = 52.5°
or
you could use the cosine law
EP^2 = 5^2+5^2-2(5)(5)cos75° = 37.059..
EP = √37.059... = appr. 6.0876
then use the Sine Law to find angle E
To find the length of FE, we already know that DE = FE. Since DE = 5, we can conclude that FE is also equal to 5.
To find the measure of angle F, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since we know that angle D is 75 degrees, we can subtract this from 180 to find the sum of angles E and F. So,
180 - 75 = 105 degrees
Since triangle DEF is an isosceles triangle, the base angles (angle E and angle F) are congruent. Therefore, we can divide the sum of angles E and F by 2 to find the measure of angle F:
105 / 2 = 52.5 degrees
So, the measure of angle F is 52.5 degrees.
To find the measure of angle E, we can subtract the measure of angle F from the sum of angles E and F:
105 - 52.5 = 52.5 degrees
So, the measure of angle E is 52.5 degrees.