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Smallest Angle in 2:3:4 (Angle) Triangle and Diagonals of a Rhombus

1. The measures of the angles of a triangle are in the ratio of 2:3:4. What is the measure of the smallest angle?

2. Each side of a rhombus measures 10 inches. If one diagonal of the rhombus is 12 inches long, what is the length of the other diagonal?

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The very, very important fact to know here is that you DO NOT NEED to know the sides of a triangle to know the angles. ALL triangles on a plane (perfectly flat surface) have angles that add up to a total of 180 degrees, always.
Since the angles are in the ratio of 2:3:4, let the angles be 2x, 3x, and 4x
So this gives you the equation 2x + 3x + 4x = 180 degrees.
Solve for x, substitute back to get each angle, and check.

Yes, the diagonals do form a vertical angle but that meand the ANGLES are equal, which does NOT tell you about the length of the sides.
I get the feeling here that you have not had lengths versus angle measure explained to you very clearly. This takes illustrations and you should go to a library or bookstore, find a basic math book or ...

Solution Summary

The Smallest Angle in 2:3:4 Triangle and Diagonals of a Rhombus are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.