University:
Carleton College
Course:
MATH 111 | Introduction to Calculus
Academic year:

2019
Views:

293

Pages:

2
Author:

StellarSymphony

HPC Law of Sines and Cosines/Area of a Triangle In-Class Applications 1. Sketch each plot of land described and find its area. From a granite post, proceed 195 ft east along Tasker Hill Road, then along a bearing of S 32° E for 260 ft, then along a bearing of S 68° W for 385 ft, and finally along a line back to the granite post. [Image of a quadrilateral with sides 195, 260, 385, and an unknown side x] x² = 195² + 260² - 2(195)(260)cos 112° x ≈ 399.2 sin θ / 195 = sin 112° / 399.2 θ = 24.5° triangle within the quadrilateral with sides 195, 260, and 399.2, with angles 112°, θ, and 24.5° Area I = 1/2 * (195)(260) * sin 112° ≈ 24828.82 ft² Area II = 1/2 * (399.2)(385) * sin 55.5° ≈ 64828.82 ft² 2. From a cement marker, proceed 260 m southwest to the river, then 240 m south along the river to the bridge, then 280 m N 40° E to a sign on the edge of Sycamore Lane, and finally along Sycamore Lane back to the cement marker. x² = 240² + 260² - 2(240)(260)cos 135° x ≈ 462 m sin θ / 240 = sin 135° / 462 θ = 21.6° triangle within the quadrilateral with sides 260, 240, and 462, with angles 135°, θ, and 21.6° Area I = 1/2 * (240)(260) * sin 135° ≈ 20940.06 m² Area II = 1/2 * (462)(280) * sin 16.6° ≈ 40540.06 m²

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