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A

Step-by-step explanation:

O = 26.6

P is a right angle so:

P = 90

angles PQO = 180

To determine Q: triangle total - (P + O)

180 - (90 + 26.6)

180 - 116.6 = 63.4

Q = 63.4

To determine side lengths: a^2 + b^2 = c^2

4^2 + b^2 = c^2

*Variable c is always hypotenuse*

Need more information so find either b or c through SOH, CAH, TOA

SOH: sine = opposite/hypotenuse

CAH: cos = adjacent/hypotenuse

TOA: tan = opposite/adjacent

tan26.6/1 = b/4

Cross multiply

1 × b = 4 × tan26.6

b = 4tan26.6

b = 2.003050791

b is about 2

b = PQ

PQ = 2

Plug b value into pythagorean theorm

4^2 + 2^2 = c^2

16 + 4 = c^2

20 = c^2

square root of 20 = square root of c^2

4.47213 = c

c is about 4.47

c = QO

Step-by-step explanation:

∠Q = 180 - 90 - 26.6

∠Q = 63.4°

side PQ

use opp. = tanФ (adj.)

PQ = tan(26.6) x 4

PQ = 2

side QO

use Pythagorean

PQ² = PO² + PQ²

PQ² = 4² + 2²

PQ =

PQ = 4.47

a

step-by-step explanation:

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