Triangle ABC is an equilateral triangle and triangle CDE is a right triangle. If the length of side AE is 20 units, what is the length of side BD?
Answers
Answer:
Step-by-step explanation:
Given : Triangle ABC is an equilateral triangle and triangle CDE is a right triangle.
the length of side AE is 20 units,
To Find : length of side BD
Solution:
Triangle ABC is an equilateral triangle
=> AB = BC = AC = 8 units
and ∠A = ∠B = ∠C = 60°
Vertically opposite angles are equal
hence ∠DCE = 60° in right angle triangle CDE
AE = AC + CE
=> 20 = 8 + CE
=> CE = 12 unit
Cos ∠DCE = DC/ CE
=> Cos 60° = DC/ 12
=> 1/2 = DC/12
=> DC = 6 units
BD = BC + CD = 8 + 6 = 14 units
Length of side BD = 14 units
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