Answer:
(a) BD = 102 cm
(b) ∠ADC = 37.8°
Step-by-step explanation:
Given kite ABCD with AB = BC = 40 cm, AD = CD = 74 cm, AC = 48 cm, you want the length of BD and the measure of angle D.
Diagonals
The diagonals of a kite cross at right angles. If we call the point of intersection E, then the Pythagorean theorem tells us ...
AE² +BE² = AB²
AE² +DE² = AD²
Using these relations, we can find BE and DE.
BE = √(AB² -AE²) = √(40² -24²) = 32
DE = √(AD² -DE²) = √(74² -24²) = 70
The length of diagonal BD is ...
BD = BE +DE = 32 +70
BD = 102 . . . . cm
Angle
DE bisects angle D. The measure of the angle can be found from the cosine relation:
cos(D/2) = DE/AD = 70/74
∠D = 2·arccos(70/74)
∠D ≈ 37.8493°
The measure of angle ADC is about 37.8°.
