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Two of the sides of a triangular garden have lengths of 100 feet and (September 2023 - G01)

Updated on 06/05/2024

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

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