Answer:
∠C = 106.7°, ∠D = 73.3°, CD = 104.4
Step-by-step explanation:
As shown in the diagram attached, let a point E be made on line BD.
Hence, BE = 130 m
BE + ED = BD
ED = BD - BE
ED = 160 m - 130 m = 30 m
Also, CE = 100 m
Using Pythagoras theorem in triangle CDE:
CD² = CE² + ED²
CD² = 100² + 30²
CD² = 10000 + 900 = 10900
CD = √10900
CD = 104.4
Using sine rule in triangle CDE:
[tex]\frac{sin(D)}{CE}=\frac{sin(E)}{CD}\\ \\sin(D)=\frac{sin(E)}{CD} *CE\\\\sin(D)=\frac{sin(90)}{104.4}*100\\ \\sin(D)=0.9578\\\\D=sin^{-1}0.9578\\\\D=73.3^o[/tex]
In trapezoid ABCD, the sum of angles in a quadralateral is 360°, hence:
∠A + ∠B + ∠C + ∠D = 360
90 + 90 + ∠C + 73.3 = 360
∠C + 253.3 = 360
∠C = 360 - 253.3
∠C = 106.7
