EXERCISE VIII. 1. In Case II. give another way of finding c, after b has been found. 2. In Case III. give another way of finding c, after a has been found. 3. In Case IV. give another way of finding b, after the angles have been found. 4. In Case V. give another way of finding c, after the angles have been found. 5. Given B and c; 6. Given B and b; 7. Given B and a; 8. Given b and c; Solve the following find A, a, b. find A, a, c. GIVEN. REQUIRED. b = 4. c = 13. A = 36°52′, B= 53°8′, c = 5. b = 10.954. c = 24.918. c = 14.290. a = 15.900, b a = 127.694, b = 20.572. b=57.386. A 34°18′, B= 55°42′, a = 12.961. 20 a = 6, c = 103. NOTE. In Cases IV. and V. the unknown side may also be found from the equations (for Case IV.) (for Case V.) b = √c2 — a2 = √(c + a) (c − a) ; These equations express the values of b and c directly in terms of the two given sides; and if the values of the sides are simple numbers (e.g. 5, 12, 13), it is often easier to find b or é in this way. But this value of c is not adapted to logarithms, and this value of b is not so readily worked out by logarithms as the value of b given under Case IV. See also § 12, Note. § 14. AREA OF THE RIGHT TRIANGLE. It is shown in Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area, F= ab. By means of this formula the area may always be found when a and b are given or have been computed. : For example: Find the area, having given: CASE I. (§ 13). A = 34° 28', c =18.75. First find (as in § 13) log a and logb. CASE IV. (§ 13). a = 47.54, c = 58.40. First find (as in § 13) log a and logb. log F= log a+ log b+colog 2 log Floga + log b+colog 2 | Solve the following triangles, finding the angles to the |