Answer:
Lengths:
PQ = PS = 4sqrt(2)
RQ = RS = 4sqrt(5)
Angles:
P: 90°
Q: 108.4°
R: 53.1°
S: 108.4°
Step-by-step explanation:
The diagonals are Perpendicular to each other
So you have 4 right angle triangles within the kite.
PQ² = 4² + 4² = 16+16
PQ = sqrt(32) = 4sqrt(2)
QR² = 4² + 8² = 16+64
QR = sqrt(80) = 4sqrt(5)
tan(Angle PSQ) = 4/4 =
PSQ = (tan^-1)(1) = 45
Angles PSQ, QPR, SPR and PQS are 45 each
So angle SPQ is 90
tan(Angle QRP) = 4/8
QRP = (tan^-1)(½) = 26.565°
Angles QRP and SRP are 26.565° each
Angle SRQ = 2(26.565) = 53.13°
Angle RQS = 90 - 26.565 = 63.435
Anges RQS and RSQ are 63.435 each
Angles PQR and PSR are:
63.435+45 = 108.445° each
