# cosine law

## 10 Solving for angle A in triangle ABC

## Solved Problem 13 | Rectangular Parallelepiped

**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.

**Solution 13**

## Problem 316 | Equilibrium of Concurrent Force System

**Problem 316**

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

## Problem 315 | Equilibrium of Concurrent Force System

**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.

## Derivation of Formula for Area of Cyclic Quadrilateral

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

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

## Trapezoidal Strip of Land from a Triangular Lot

**Problem**

A strip of 640 m^{2} 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

## Derivation of Cosine Law

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

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

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

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