Question

(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

Answer 1

thats better thank you

In this case we must use the cosines theorem

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

now use this formula to find every angle

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

DO THE SAME FOR THE OTHER 3

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

LASTLY P

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

The greatest angle will be P