Can anybody help me with trying to figure out how to do this?

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:

=> 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:

=> CD ≈ 41.39

f. BD = 22. 94 (part d)

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

christopher is 272,195 year old

step-by-step explanation: