(10) Side adjacent = side opposite tangent

(11) Hypotenuse = side opposite sine

(12) Hypotenuse = side adjacent cosine

f.

Procedure for using these Rules.

(1) In a right triangle, both the known and unknown sides (opposite,

adjacent, and hypotenuse) of the problem are named.

(2) Choose from among the previous rules; select one that fits the given

numerical values.

(3) Substitute the given values in the rule and solve for the unknown.

EXAMPLE

Find side "a" if sin A = 3/5 and side "c" = 20.5 (figure 14 on the following

page).

Here the sine of angle A is given, and "a" is the side opposite.

According to rule (5) in paragraph 3e on page 53, side opposite = hypotenuse

x sine. Substituting 20.5 for hypotenuse and 3/5 for sine, we get: side

opposite = 20.5 x 3/5 = 12.3.

Find "b" if cos A = .44 and "c" = 3.5 (figure 15 on the following page).

Here the cosine of angle A is given, and "b' is the side adjacent.

According to rule (8) in paragraph 3e on page 53, side adjacent = hypotenuse

x cosine.

Substituting 3.5 for hypotenuse and .44 for cosine, the side

adjacent = 3.5 x .44 = 1.54.

Find "a" if tan A = 11/3 and "b" = 2 5/11 (figure 16 on page 56). Here the

tangent of angle A is given, and "a" is the side opposite.

According to

rule (6) in paragraph 3e on page 53, side opposite = side adjacent x

tangent. Substituting 2 5/11 for side adjacent and 11/3 for tangent, side

opposite = 2 5/11 x 11/3 = 9.

Find "b" if cot A = 4 and "a" = 17 (figure 17 on page 56).

Here the

cotangent of angle A is given, and "b" is the side adjacent. According to

rule (9) in paragraph 3e on page 53, side adjacent = side opposite x

cotangent.

Substituting 17 for side opposite and 4 for cotangent, side

adjacent = 17 x 4 = 68.

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