Whether the statement “Any triangle , right or oblique, can be solved if at least one side and any other two measures are known” is true or false.

Question

Want to see more full solutions like this?

Answer 1

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8, Problem 1MC

To determine

Whether the statement “Any triangle, right or oblique, can be solved if at least one side and any other two measures are known” is true or false.

Expert Solution & Answer

Answer to Problem 1MC

The given statement is true_.

Explanation of Solution

In a triangle, if one measure is a side, then the other two possible measures are side and side, side and angle, angle and angle.

If two possibilities are sides, then triangle has three sides. That is, SSS.

If three sides are known, then will draw triangle.

If two possibilities are angles, then triangle has one side and two angles. That is, AAS.

If one side and two angles are known, then will draw triangle.

If two possibilities are angles, then triangle has one side and two angles. That is, ASA.

If one side and two angles are known, then will draw triangle.

If two possibilities are one angle and one side, then triangle has one side and two angles. That is, SAS.

If one angle and two sides are known, then will draw triangle.

If two possibilities are one angle and one side, then triangle has one side and two angles. That is, SSA.

If one angle and two sides are known, then will draw triangle.

Therefore, the statement “Any triangle, right or oblique, can be solved if at least one angle and any other two measures are known” is true_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Într-un bloc sunt apartamente cu 2 camere și apartamente cu 3 camere , în total 20 de apartamente și 45 de camere.Calculați câte apartamente sunt cu 2 camere și câte apartamente sunt cu 3 camere.

1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k components, where k is the greatest common divisor of {n, r,s}.

Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]

Answer 2