Filling in the above outline, the completed work appears as follows:

Since the check formula gives the same value for log a as that found in the solution, the computation is in all probability correct.

2. In a right triangle, given c = 6.275, ẞ= 18° 47', to find

Solve the following right triangles, y being the right angle. It is recommended that the first ten problems be solved by the use of a three-place table of natural functions, or by means of a slide rule.

The following problems should be solved by the use of

* Whenever sides are given to four significant figures and angles to

minutes.

31. Solve the isosceles triangle, one of the equal sides being 690.13, and one of the base angles being 15° 20' 25".

32. Solve the isosceles triangle whose altitude is 606.6, one of the equal sides being 955.7.

33. Solve the isosceles triangle whose base is 2558, and whose vertical angle is 104° 0' 46".

34. Solve the isosceles triangle whose base is 161.4, and whose altitude is 204.4.

35. Find the length of a side of a regular octagon inscribed in a circle whose radius is 49.

37. Oblique triangles. When any three independent parts of an oblique triangle are given it can be solved by means of right triangles. The oblique triangle may be divided into two right triangles by drawing a perpendicular from one vertex to the opposite side, or the opposite side produced.

When one of the given parts is an angle, the perpendicu、 lar must be selected so that one of the resulting right triangles will contain two of the given parts.

the right triangles can be obtained by equating the expres sions for the length of the perpendicular obtained from each right triangle.

1. To find the distance from B to C, two points on opposite sides of a river, a line BA, 200 feet long, was laid off at right angles to the line BC, and the angle BAC was measured and found to equal 55° 29'. What was the required distance?

2. A railway is inclined 4° 23' 20" to the horizontal. How many feet does it rise per mile, measured along the horizontal?

3. From the top of a tower 120 feet high the angle of depression of an object in the horizontal plane of the base of the tower is 24° 27'. How far is the object from the foot of the tower? How far from the observer?

Given any point A and a second point B at a greater elevation than A.

A

В

B

The angle of elevation of B from A is the angle that the line AB makes with its orthogonal projection upon the horizontal plane through A. In the figure it is the angle a.

The angle of depression of A from B is the angle that the line BA makes with its orthogonal projection upon the horizontal plane through B. In the figure it is the angle ẞ. It is clear that α = B.

4. Find the length of one side of a regular pentagon inscribed in a circle whose radius is 18.24 feet.

5. Find the perimeter of a regular polygon of n sides inscribed in a circle whose radius is r.