Solve for the unknown sides(2) and all angle measurements(4) in a kite

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

898.1666667

step-by-step explanation:

5389/6 = 898.1666667