MATH SOLVE

2 months ago

Q:
# In △POK PK = KO = 11, m∠K = 145º. Find altitude PH.

Accepted Solution

A:

The length of the altitude PH is 6.31 unitsStep-by-step explanation:Look to the Attached figure1. PK = KO = 112. m∠K = 145°3. The altitude PH is out side the triangle because angle K is obtuseWe can find the altitude PH by using the trigonometry functionsin 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 = 6.31The length of the altitude PH is 6.31 unitsLearn more:You can learn more about the triangles in brainly.com/question/6530759#LearnwithBrainly