(G.5.b, 1pt) A sports photographer made a scale drawing of a hockey rink to study shooting angles from 3 different locations: the players' bench (B), the penalty box (P), and the north goal judge's box (N). Determine which of these angles has the greatest measure. P 110 it N 95 ft S 130 ft B Ο Α. ΖΝ B. ZS O C. ZP O D. ZB

Respuesta :

thats better thank you

In this case we must use the cosines theorem

[tex]\begin{gathered} a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos A \\ FIND\text{ A} \\ A=\cos ^{-1}(\frac{b^2+c^2-a^2}{2\cdot b\cdot c}) \end{gathered}[/tex]

now use this formula to find every angle

[tex]\begin{gathered} a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos A \\ FIND\text{ B} \\ B=\cos ^{-1}(\frac{130^2+95^2-110^2}{2\cdot130\cdot95}) \\ B\approx55.96 \end{gathered}[/tex]

DO THE SAME FOR THE OTHER 3

[tex]\begin{gathered} a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos A \\ FIND\text{ N} \\ N=\cos ^{-1}(\frac{130^2+110^2-95^2}{2\cdot130\cdot110}) \\ N\approx45.70 \end{gathered}[/tex]

LASTLY P

[tex]\begin{gathered} a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos A \\ FIND\text{ P} \\ P=\cos ^{-1}(\frac{110^2+95^2-130^2}{2\cdot110\cdot95}) \\ P\approx78.34 \end{gathered}[/tex]

The greatest angle will be P