Question

for which purpose is the asa method especially useful in practical applications?
a. surveying
b. machinery assembly
c. architectural design
d. electronic circuit design

when using the asa method, what is the significance of the included side?
a. it connects the two given angles
b. it is the longest side of the triangle
c. it is always horizontal
d. it determines the height of the triangle

which method requires two sides and the included angle to construct a triangle?
a. asa
b. esa
c. sss
d. sas

Explanation:

• First question: The ASA (Angle - Side - Angle) method is very useful in surveying. In surveying, when we know two angles and the included side (ASA), we can calculate distances and positions of points on the ground. For example, if we know the angles from two different points of observation to a distant object and the distance between the two points of observation (the included side), we can use trigonometric laws (based on ASA principles) to find the distance to the object.
• Second question: In the ASA method, the included side connects the two given angles. By having the side between the two angles, we can use the law of sines or cosines (in the context of triangle congruence and construction) to fully define the triangle. If the side was not connecting the two angles (i.e., not included), we would not be able to uniquely construct the triangle using the ASA criteria.
• Third question: The SAS (Side - Angle - Side) method requires two sides and the included angle to construct a triangle. The ASA method requires two angles and the included side. The SSA (Side - Side - Angle) is not a valid congruence criterion in general (except for the right - triangle case with the hypotenuse - leg theorem). The SSS (Side - Side - Side) requires three sides.

Answer:

1. A. Surveying
2. A. It connects the two given angles
3. D. SAS