Trigonometry help, please!!!?

Question

I need to solve a triangle using trigonometric functions...I've only been given an angle and the length of the side opposite the angle, How do I find the side length adjacent to the angle and the length of the hypotenuse?

Answer 1

sine(angle) = opposite/hypotenuse

Answer 2

You mensions "hypotenuse",so the triangle ABC must be a rt.<

triangle. Let C=90*,A and its opposite side a are known,then angle

B can be found : B=180*-C-A=180*-90*-A=

90*-A.

Since tanB=b/a

=>b=a* tan(90*-A) (where b is the side opposite to B)

=>b=a*cotA (b can be worked out for a,A are given)

c is the hypotenuse which can be found by

a/c=sinA or

c=a/sinA

Answer 3

GIVEN --

Angle and length of side opposite the angle

REQ'D --

Length of side adjacent to the angle

Length of the hypotenuse

Let

A = value of the angle given

a = length of the side opposite the angle

b = length of side adjacent to the angle

c = hypotenuse

SOLUTION:

tan A = (a/b), hence

b = a/(tan A)

For the length of the hypotenuse, there are two ways to solve this. First solution,

sin A = (a/c)

c = a/(sin A)

OR, the second solution to determine "c" is to simply use the Pythagorean theorem. Since sides "a" and "b" are known, then

c = sqrt(a^2 + b^2)

Hope this helps.

Answer 4

You have more than you think.  You mentioned the hypotenuse.  So you have a second angle as well, a right angle.  With two angles you can calculate the third since all triangles have 180°.  Then use the Law of Sines to get the second side and the Pythagorean Theorem to get the third side.