Machinery's Handbook, 31st Edition
Solution of Right Triangles 99 tables, either when given an angle and seeking a trigonometric ratio, or “in reverse,” when given a ratio (side lengths) and seeking an angle. A full explanation of trigonometric func- tions and the use of their tables begins on page 105. Solution and Examples of Right Triangles (US Customary or Metric Units) Examples below show angle measure further divided into units of minutes ( ′ ) and seconds ( ″ ). 1º = 60 ′ ; 1 ′ = 60 ″ , rather than decimal parts.
c = 22 inches; B = 41 ° 36 ′ a c B cos 22 = =
41 ° cos 36 ′ × 22 0.74780 × =
a
= 16.4516 in. b c B sin 22 41 ° sin 36 ′ × 22 0.66393 × = = = = 14.6065 in. A 90 ° B – 90 ° 41 ° 36 ′ – 48 ° 24 ′ = = =
C 90°
A
b
Hypotenuse and One Acute Angle Known
c = 25 centimeters; a = 20 centimeters b c 2 a 2 – 25 2 20 2 – = = = = 225 = 15 cm
625– 400
b
B A 90° c 25 Hypotenuse and One Side Known
a c -- 20 25 --- 0.8 = = =
A sin
53 ° 8 ′ = B 90 ° A – 90 ° 53 ° 8 ′ – 36 ° 52 ′ = = = sin –1 (0.8) =
Hence, A
a = 36 mm; b = 15 mm c a 2 b 2 + = =
b 15
A
36 2 15 2 + = = 1521 = 39 mm
1296+225
B
a 36
a b -- 36 15 --- 2.4 = = =
c
A tan
67 ° 23 ′ = B 90 ° A – 90 ° 67 ° 23 ′ – 22 ° 37 ′ = = = tan –1 (2.4) =
Hence, A
Two Sides Known
a = 12 meters; A = 65 ° c a 12 65 ° sin -------- = =
12 0.90631 ---------- 13.2405 m =
A sin ------ A tan ------
=
c
B
b = 5.5957 B 90 ° A – 90 ° 65 ° – 25 ° = = = a = = m
12 65 ° cot × 12 0.46631 × =
b
One Side and One Angle Known
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