In triangle ΔABC, ∠C is a right angle and

CD

is the altitude to

AB

. Find the measures of the angles of the ΔCBD and ΔCAD if:

m∠A = 20°

Step-by-step explanation:

Refer to the figure shown below.

Given:

m∠C = 90°, because ∠C is a right angle.

m∠D = 90°, because CD is the height to AB.

m∠A = α

Because the sum of angles in a triangle is 180°, therefore

m∠DBC + 90° + α = 180°

m∠DBC = 90° - α

Again, for the same reason,

m∠DCB + m∠DBC + 90° = 180°

m∠DCB + 90° - α + 90° = 180°

m∠DCB = α

For the same reason,

m∠ACD + 90° + α = 180°

m∠ACD = 90° - α

m∠ADC = 90° (by definition)

m∠CDB = 90° (by definition)

m∠DBC = 90° - α

m∠DCB = α

m∠CDB = 90°

m∠ACD = 90° - α

m∠ADC = 90°

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.