The length of the altitude PH is 6.31 units
Step-by-step explanation:
Look to the Attached figure
1. PK = KO = 11
2. m∠K = 145°
3. The altitude PH is out side the triangle because angle K is obtuse
We can find the altitude PH by using the trigonometry functions
in Δ PHK
∵ O, K , H are on the same line
∴ m∠OKP + m∠PKH = 180° ⇒ straight angle
∵ m∠ OKP = 145° ⇒ given
∴ 145 + m∠PKH = 180
- Subtract 145 from both sides
∴ m∠PKH = 35°
In Δ PKH
∵ m∠H = 90°
∵ m∠PKH = 35°
∵ PK = 11
- By using sine function sinФ = opposite/hypotenuse
∵ Ф = 35° , opposite is PH , hypotenuse is PK
∵ sin(35) = [tex]\frac{PH}{PK}[/tex]
∴ sin(35) = [tex]\frac{PH}{11}[/tex]
- By using cross multiplication
∴ PH = 11 sin(35)
∴ PH = 6.31
The length of the altitude PH is 6.31 units
Learn more:
You can learn more about the triangles in brainly.com/question/6530759
#LearnwithBrainly
