Utilizing the Law of Sines (sinA/a=sinB/b=sinC/c) and recognizing that the angles in a triangle add up to 180°.
The angle C calculates to 180-53-17=110°
Thus, we have 27/sin53=b/sin17=c/sin110
This leads to b=27sin17/sin53, c=27sin110/sin53
The perimeter is defined as a+b+c, so
p=27+27sin17/sin53+27sin110/sin53 units
p≈68.65 units (rounded to the nearest hundredth of a unit)
The diagonal measures 20.68 ft; the shorter base is 17.21 ft. To understand this, we recognize that with base angles summing to 140°, each angle is 70°, given the isosceles trapezoid's properties. We can apply the Law of Cosines to find the diagonal's length, denoted as d. The length of the diagonal determines to be d = 20.68 ft. Determining the shorter base is somewhat more complex. By drawing an altitude from the upper vertices to the base, which measures 22 ft, we create two similar smaller right triangles requiring us to find the height and base measures related to each of the 70-degree angles and the hypotenuse of 7. By working through the calculations for height and base from one triangle, we subsequently find that 22 minus twice the base measure gets us to the shorter base's measure, arriving at x = 17.21 ft.
To tackle this sinusoidal question, we begin with the following: Using the formula; g(t)=offset+A*sin[(2πt)/T+Delay] According to sinusoidal theory, the duration from trough to crest is typically half of the wave's period. Here, T=2.5 The peak magnitude is calculated as: Trough-Crest=2.1-1.5=0.6 m amplitude=1/2(Trough-Crest)=1/2*0.6=0.3 The offset from the center of the circle becomes 0.3+1.5=1.8 As the delay is at -π/2, the wave will commence at the trough at [time,t=0]. Plugging these values into the formula gives: g(t)=1.8+(0.3)sin[(2*π*t)/2.5]-π/2] g(t)=1.8+0.3sin[(0.8πt)/T-π/2]
