cosine law

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.
 

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
 

Quadrilateral is a polygon of four sides and four vertices. It is also called tetragon and quadrangle. For triangles, the sum of the interior angles is 180°, for quadrilaterals the sum of the interior angles is always equal to 360°
 

Classifications of Quadrilaterals
There are two broad classifications of quadrilaterals; simple and complex. The sides of simple quadrilaterals do not cross each other while two sides of complex quadrilaterals cross each other.
 

Simple quadrilaterals are further classified into two: convex and concave. Convex if none of the sides pass through the quadrilateral when prolonged while concave if the prolongation of any one side will pass inside the quadrilateral.
 

The following formulas are applicable only to convex quadrilaterals.
 

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.
 

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

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.
 

The Six Trigonometric Functions

1. $\sin \theta = \dfrac{a}{c}$
2. $\cos \theta = \dfrac{b}{c}$
3. $\tan \theta = \dfrac{a}{b}$
4. $\csc \theta = \dfrac{c}{a}$
5. $\sec \theta = \dfrac{c}{b}$
6. $\cot \theta = \dfrac{b}{a}$