Answer:
The length of EF = 7.48 feet
Step-by-step explanation:
* Lets consider these tree segment formed triangle DEF
- We have the length of two sides and the measure of the
including angle between these two sides
* So we can use the cos Rule to find the length of the third side
- The cos rule ⇒ a² = b² + c² - 2bc cosA
# a is the side opposite to angle A
# b is the side opposite to angle B
# c is the side opposite to angle C
# Angle A is the including angle between b and c
* In the problem
∵ DE = 6 feet
∵ DF = 11 feet
∵ m∠FDE = 40° ⇒ including angle between DE and DF
and opposite to EF
- By using cos Rule
∴ (EF)² = (DE)² + (DF)² - 2(DE)(DF) cos∠FDE
∴ (EF)² = (6)² + (11)² - 2(6)(11) cos(40)
∴ (EF)² = 55.882133 ⇒ take square root for both sides
∴ EF = 7.47543 ≅ 7.48 feet
* The length of EF = 7.48 feet
