Question

1. why is the sas method common in bridge design? a. it only uses angles for construction. b. it ensures stability by relying on fixed angles and sides. c. it minimizes the number of measurements needed. d. it allows for flexibility in side lengths. 17. which scenario best illustrates the use of the asa method? a. mapping land with fixed side lengths b. determining the height of a triangular structure c. calculating the longest diagonal in a square d. designing a triangular stage platform with specific angles and one known side 18. a ladder leaning against a building creates a right - triangle with the ground. the ladder is 20 ft long, and the base of the ladder is 16 ft from the building. how high does the ladder reach on the building? a. 12 ft b. 10 ft c. 11 ft d. 15 ft

Explanation:

16.

The SAS (Side - Angle - Side) method ensures stability in bridge design as fixed angles and side - lengths create rigid triangular structures. Triangles are inherently stable shapes in construction.

The ASA (Angle - Side - Angle) method is used when two angles and the included side are known. Designing a triangular stage platform with specific angles and one known side fits this method as it involves two angles and the side between them for construction.

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder), \(a\) is the distance from the base of the ladder to the building, and \(b\) is the height the ladder reaches on the building. Here, \(c = 20\) ft and \(a=16\) ft. We need to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(b=\sqrt{20^{2}-16^{2}}=\sqrt{(20 + 16)(20 - 16)}=\sqrt{36\times4}=\sqrt{144}=12\) ft

Answer:

b. It ensures stability by relying on fixed angles and sides.

17.