The length of PQ is 19.66 units
Step-by-step explanation:
The given is:
1. PK = KQ = 12
2. m∠P = 35º
We need to find the length pf PQ
∵ PK = KQ
∴ m∠P = m∠Q
∵ m∠P = 35°
∴ m∠Q = 35°
The sum of measures of the angles of a triangle is 180°
∴ m∠P + m∠Q + m∠K = 180°
∴ 35 + 35 + m∠K = 180
∴ 70 + m∠K = 180
- Subtract 70 from both sides
∴ m∠K = 110°
Let us use cosine rule to find the length of PQ
∵ PQ = [tex]\sqrt{(KP)^{2}+(KQ)^{2}-2(KP)(KQ)cos(K)}[/tex]
∵ PK = 12 , KQ = 12 , m∠K = 110°
- Substitute these values in the rule
∴ PQ = [tex]\sqrt{(12)^{2}+(12)^{2}-2(12)(12)cos(110)}[/tex]
∴ PQ = 19.66
The length of PQ is 19.66 units
Learn more:
You can learn more about triangle in brainly.com/question/12985572
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