Pregunta
Which of the following TWO statements are correct regarding unique triangles?
A. No triangle can be constructed with side lengths of 15 cm and 21 cm and an included angle measure of
B. Exactly 1 triangle can be constructed with side lengths of 15 cm and 21 cm and an included angle measure of
C. More than 1 triangle can be constructed with side lengths of 15 cm and 21 cm and an included angle measure of
D. No triangle can be constructed with angle measures of
E. Exactly 1 triangle can be constructed with angle measures of
F. More than 1 triangle can be constructed with angle measures of
A. Side lengths of 3 inches, 4 inches, and 5 inches.
B. Angle measures of
C. Side lengths of 2 inches and 5 inches with an included angle of
D. Angle measures of
E. Side lengths of 4 cm and 6 cm with a non included angle measure of
A. No triangle can be constructed with side lengths of 15 cm and 21 cm and an included angle measure of
B. Exactly 1 triangle can be constructed with side lengths of 15 cm and 21 cm and an included angle measure of
C. More than 1 triangle can be constructed with side lengths of 15 cm and 21 cm and an included angle measure of
D. No triangle can be constructed with angle measures of
E. Exactly 1 triangle can be constructed with angle measures of
F. More than 1 triangle can be constructed with angle measures of
A. Side lengths of 3 inches, 4 inches, and 5 inches.
B. Angle measures of
C. Side lengths of 2 inches and 5 inches with an included angle of
D. Angle measures of
E. Side lengths of 4 cm and 6 cm with a non included angle measure of
Ask by Sullivan Murphy. in the United States
Jan 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
First Part:
- B. Exactly 1 triangle can be constructed with side lengths of 15 cm and 21 cm and an included angle measure of
. - D. No triangle can be constructed with angle measures of
and and a side length of 4 inches.
Second Part:
- A. Side lengths of 3 inches, 4 inches, and 5 inches.
- C. Side lengths of 2 inches and 5 inches with an included angle of
. - D. Angle measures of
and with an included side that is 9 cm long.
Solución
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Como
The Deep Dive
In triangle construction, the Side-Angle-Side (SAS) condition guarantees that a triangle can be uniquely determined when two sides and the included angle are known. With side lengths of 15 cm and 21 cm and an included angle of
To ensure a unique triangle, the combination of two sides and the included angle is often decisive. For instance, option A (3 inches, 4 inches, and 5 inches) adheres to the Pythagorean theorem, forming a right triangle. Similarly, option C with 2 inches, 5 inches and a
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