cosine law | MATHalino reviewer about cosine law

Problem 10
In a triangle ABC, if $\dfrac{2 \cos A}{a} + \dfrac{\cos B}{b} + \dfrac{2 \cos C}{c} = \dfrac{a}{bc} + \dfrac{b}{ca}$ , find the value of angle $A$ .

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Problem 13
The figure represents a rectangular parallelepiped; AD = 20 in., AB = 10 in., AE = 15 in.
(a) Find the number of degrees in the angles AFB, BFO, AFO, BOF, AOF, OFC.
(b) Find the area of each of the triangles ABO, BOF, AOF.
(c) Find the perpendicular distance from B to the plane AOF.

Area, angle, and distance in rectangular parallelepiped.

Solution 13

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Problem 316
Determine the values of α and θ so that the forces shown in Fig. P-316 will be in equilibrium.

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Problem 315
The 300-lb force and the 400-lb force shown in Fig. P-315 are to be held in equilibrium by a third force F acting at an unknown angle θ with the horizontal. Determine the values of F and θ.

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For a cyclic quadrilateral with given sides a, b, c, and d, the formula for the area is given by

$A = \sqrt{(s - a)(s - b)(s - c)(s - d)}$

Where s = (a + b + c + d)/2 known as the semi-perimeter.

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Problem
A strip of 640 m² is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.

A. 7.1 m
B. 8.1 m
C. 8.7 m
D. 7.7 m

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The following are the formulas for cosine law for any triangles with sides a, b, c and angles A, B, C, respectively.

$a^2 = b^2 + c^2 - 2bc\cos A$

$b^2 = a^2 + c^2 - 2ac\cos B$

$c^2 = a^2 + b^2 - 2ab\cos C$

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