Plane trigonometry with practical applications, by Leonard E. Dickson.

22

TRIGONOMETRY

[Art. 14

Second, let the two given parts be an angle and a side. Since
A + B = 90~, we have both angles. Then two of the relations
(1) determine the two unknown sides and the third relation
serves as a check.
Besides the check mentioned, a further check against gross
errors may be secured by inspecting Traverse Table VI, to be
explained in Chapter III, or by making a drawing to scale.
EXAMPLE 1. Given ZA = 43~15' and the hypotenuse c = 13.20, find the
remaining parts of the right triangle.
Solution. B = 90~ - A = 46~45'.. a A.. b
sin A = a c sin A cos A =,= c cos A
c c
sin A = 0.6852 cos A = 0.7284
c= 13.2 c = 13.2
13704 14568
20556 21852
6852 7284
a = 9.0446 b = 9.6149
Since only four decimal places of sin A and cos A were given by our tables,
we have suppressed the fifth decimal places in the products. Check: tan A =
0.9408 = a/b.
EXAMPLE 2. Given the hypotenuse c = 63.12 and a leg a = 47.04, find the
remaining parts of the right triangle.
Solution. First find ZA from sin A = a/c:
47.04
sin A = 6312 0.7452, A = 48~10~'.
Next find b from cos A = b/c:
b = c cos A = 63.12 X 0.6669 = 42.09.
As a check, compute b directly from the given parts, using
(2) b2= (c +a) (c-a),
which is a way of writing a2 + b2 = c2.
EXAMPLE 3. Given a = 27, b = 40, find the remaining parts.
Solution. tan A = 27/40 = 0.6750, A = 34~1', B = 55~59'.
c2 = a2+ b2 =729 + 1600 = 2329, c =48.260.
Check: cos A = 0.8288 = b/c.
The method of Ex. 3 is not recommended when either leg is expressed by a
number containing more than two digits.