Kalah M.
asked • 04/16/19Can a triangle be formed?
The triangle described is of the form SSA. Determine if there is no triangle possible, one triangle possible, or two triangles possible. If only one triangle is possible, solve the triangle. If either two triangles may be formed or no triangle may be formed, say so. The triangle is defined by b=40, c=50, y=25 degrees
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1 Expert Answer
William W. answered • 04/16/19
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Experienced Tutor and Retired Engineer
Step 1) Find h: In this case use sin25° = h/40 or h = 16.9
Step 2) Decide which case you have below:
Case 1) If a<h, no triangle. That's not the case here.
Case 2) If a is between h and b the there are two triangles. That is not the case here.
Case 3) If a = h or if a > b, the one triangle. That is the case here
One triangle
Kalah M.
Thank you!
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04/17/19
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Sam Z.
To label a triangle "a" is the shortest side; "b" mid-length; "c" hypotenuse. Angle (alpha) opposite side "a"; (beta) opposite side "b"; (gamma) opposite side "c". I take it "y" is angle (beta). The formula I'm using is: (beta)=acos((a^2+c^2-b^2)/(2ac)) so 25=acos((a^2+50^2-40^2)/(2a50)) a=11.36 (alpha)=acos((b^2+c^2-a^2)/(2bc)) so (alpha)=acos((40^2+50^2-11.36^2)/(2*40*50)) (alpha)=6.91 180-6.91-25=148.1=(gamma).04/16/19