Section: Math 0 Likes
Two of the sides of a triangular garden have lengths of 100 feet and (September 2023 - G01)
Two of the sides of a triangular garden have lengths of 100 feet and 80 feet, respectively. The angle formed by these 2 sides measures 60°. Which of the following is closest to the length, in feet, of the 3rd side of the garden?
(Note: The law of cosines states that for any triangle with vertices A, B, and C, where the sides opposite those vertices have lengths a, b, and c, respectively, c^2=a^2+b^2-2abcos C; cos 60°=0.5.)
A. 60
B. 90
C. 92
D. 120
E. 156
Solution
Correct answer: C. 92.
Step 1: Identify the known values
- Side A = 100 feet
- Side B = 80 feet
- Angle C = 60°
Step 2: Apply the Law of Cosines
$$c^2 = a^2 + b^2 - 2ab\cos C$$
$$c^2 = 100^2 + 80^2 - 2(100)(80)(0.5)$$
Step 3: Calculate the length of the 3rd side
$$c = √(10000 + 6400 - 8000) = √(8400) \approx 92$$
Therefore, the closest answer is C. 92.
Exam Edition: September 2023 - G01
Exam Year: 2023
Related topics: Geometry, Trigonometry, Algebra