The Given Measurements May or May Not Determine a Triangle $$\mathrm { A } = 39 ^ { \circ } , \mathrm { b } = 15 , \mathrm {~B} = 28 ^ { \circ }$$

question 279

Multiple Choice

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is
formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
- $$\mathrm { A } = 39 ^ { \circ } , \mathrm { b } = 15 , \mathrm {~B} = 28 ^ { \circ }$$

• A) \(\mathrm { C } = 113 ^ { \circ } , \mathrm { a } \approx 11.2 , \mathrm { c } \approx 7.7\)
• B) The triangle cannot be solved with the Law of Sines.
• C) No triangle is formed.
• D) \(\mathrm { C } = 113 ^ { \circ } , \mathrm { a } \approx 20.1 , \mathrm { c } \approx 29.4\)

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Definitions:

Von Neumann-Morgenstern

Pertains to a theorem used in expected utility theory, which provides an axiomatic basis for the selection of optimal choices under uncertainty.

Utility Function

An economic model that quantifies the satisfaction or happiness a consumer receives from consuming goods and services.

Expected Utility

A theory in economics that models how agents choose among risky alternatives to maximize their satisfaction.

Income

Receipts garnered on a habitual basis as a result of engaging in work or investment.