TRIGONOMETRICAL PROPOSITIONS. 67
10.Given A D, & the angle D with the side A B, to find the angle A.
Multiply radius by the sine of the complement of A D, divide the product by the tangent of the complement of D, and the tangent of the complement of C A D will be produced, giving us C A D. Again, multiply the tangent of A D by the sine of the complement of C A D, divide the product by the tangent of A B, and the sine of the complement of B A C will be produced, giving B A C. Then the sum or difference of the ares B A C and C A D will be the required angle B A D.
11.Given A D, & the angle D with the angle A, to find the side A B.
Multiply radius by the sine of the complement of A D, divide the product by the tangent of the complement of D, and you have the tangent of the complement of C A D; C A D being thus known, the difference or sum of the same and the whole angle A is the angle B A C. Multiply the tangent of A D by the sine of the complement of C A D; divide the product by the sine of the complement of B A C, and you will have the tangent of A B.
12.Given A D, & the angle D with the angle A, to find the third angle B.
Multiply radius by the sine of the complement of A D, divide the product by the tangent of the complement of D, and the sine of the complement of B will be produced, from which we have the angle required.
Given A D, & the angle D with the angle A, to find the side B D.
This follows from the above, but in this form the problem would require the: “Rule of Three” be
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