Given that ...
a = 16
b = 18
A = 60 Degrees
Determine if there is:
a) One triangle
b) Two triangles
c) No triangles
I don't know how to set this problem up, or how to figure it out, any help would be greatly appreciated to get me started..Thanks.
2007-01-11 02:00:20 · 6 answers · asked by Matthew B 2 in Science & Mathematics ➔ Mathematics
I believe it's one but not sure how to prove it..
2007-01-11 02:01:00 · update #1
sin(60)/16=sin(B)/18
sin(B)=sin(60)*18/16=.97
B=77 or 103
C=180-77-60=43 works
C=180-103-60=17 works also
2 triangles
2007-01-11 02:09:54 · answer #1 · answered by Professor Maddie 4 · 0⤊ 0⤋
You have to graph this. Draw a horizontal line 18 cm long. At the right end draw a line such that the angle on the left is 60 degrees. At the left end draw a circle 16 cm of radius.
Either this circle is
a) tangent with the 60 degree slope or
b) it intersects twice
c) it never intersects
Lets check for the tangent. If it is tangent, then it creates a right angle. In which case you can use the law of sines to get the radius
r = 18* sin(60) = 15.58 which is not equal to 16.
So it is not one. And since our side is 16 cm, it is longer than 15.58 and will intersect the circle twice. So the answer is 2.
2007-01-11 10:16:37 · answer #2 · answered by catarthur 6 · 0⤊ 0⤋
you have to use Sine Law to determine how many triangles can be formed.
recall:
sine law states that (sin A)/a = (sin B)/b = (sin C)/c, where A, B and C are the angles of the triangle, and a, b, c are the corresponding sides.
plug in the values that are given..
(sin 60)/16 = sin B / 18
sqrt(3)/32 = sin B/18
9 sqrt(3)/16 = sin B
B = 76.98 degrees
so a triangle can be formed
2007-01-11 10:13:29 · answer #3 · answered by january 2 · 0⤊ 0⤋
You have 2 sides and 1 angle - you need 3 sides or 3 angles to make a triangle so I reckon it's just an angle i.e.no triangles
2007-01-11 10:09:56 · answer #4 · answered by anabelezenith 3 · 0⤊ 0⤋
This describes one triangle.
By geometric theory, a triangle can be uniquely defined by:
- three sides
- two sides and one angle
- two angles and one side
Three angles does not describe one triangle, but instead infinite triangles all similar in shape, but varying in size.
2007-01-11 10:12:06 · answer #5 · answered by Dave 6 · 0⤊ 0⤋
You are correct in saying that its one. To prove it, you would have to use Pythagorean Therom (add the sides).
2007-01-11 10:04:26 · answer #6 · answered by Giant Squid Man 2 · 0⤊ 0⤋