Answer:
a. Angle A = 35
As triangle ABD has angle ADB equal to 90°
=> ABD is the right triangle
=> Angle ABD + Angel A = 90°
=> Angel A = 90° - Angel ABD = 90°- 55° = 35°
So Angel A = 35°
b. Angle CBD = 61
As triangle BDC has angle BDC equal to 90°
=> BDC is the right triangle
=> Angle CBD + Angel C = 90°
=> Angel CBD = 90° - Angel C = 90°- 29° = 61°
So Angel CBD = 61°
c. AD = 32.77
As ABD is the right triangle, so that we have the formula:
sin (an angel) = opposite side/ hypotenuse
=> sin angel ABD = AD/ AB
=> AD = sin angel ABD x AB = sin 55° x 40 ≈ 32.77
So AD = 32.77
d. BC = 47.32
As ABD is the right triangle, according to Pythagoras theorem, we have:
[tex]BD^{2} = AB^{2} -AD^{2} =40^{2} - 32.77^{2} = 1600-1073.8729 = 526.1271[/tex]
=> BD ≈ 22.94
As BCD is the right triangle, so that we have the formula:
sin (an angel) = opposite side/ hypotenuse
=> sin angel C = BD/ BC
=> BC = BD/ sin angel C = 22.94 / sin 29° ≈ 47.32
So BC = 47.32
e. CD = 41.39
As BCD is the right triangle, according to Pythagoras theorem, we have: [tex]CD^{2} = BC^{2} - BD^{2} =47.32^{2} -526.1271= 2239.1824-526.1271=1713.0553[/tex]
=> CD ≈ 41.39
f. BD = 22. 94 (part d)
