4.11

Picture...https://static.k12.com/nextgen_media/assets/8107320-NG_GMT_DP024_232_008.jpg

3. What is the measure of ∠Y ?

Round your answer to the nearest degree.

24°

26°

59°

61°

$\begin{array}{|rcll|} \hline \dfrac{ \sin(Y) } {35.2} &=& \dfrac { \sin(95^{\circ})} {86} \\ \sin(Y) &=& \dfrac { 35.2\cdot \sin(95^{\circ})} {86} \\\\ \sin(Y) &=& 0.40774480666 \\\\ \angle{Y} &=& 24.0632455972^{\circ} \\ \hline \end{array}$

$\angle{Y} = 24^{\circ}$

Picture...https://static.k12.com/nextgen_media/assets/8107323-NG_GMT_DP024_232_011.jpg

4. What is the value of g?

Round your answer to the nearest tenth.

18.6 ft

20.4 ft

21.4 ft

24.0 ft

$\begin{array}{|rcll|} \hline g^2 &=& 25^2+32^2-2\cdot 25\cdot 32\cdot \cos(42^{\circ}) \\ g^2 &=& 1649- 1600\cdot 0.74314482548 \\ g^2 &=& 1649- 1189.03172076 \\ g^2 &=& 459.968279236 \\ g &=& 21.4468710827\ \text{ft} \\ \hline \end{array}$

$g = 21.4\ \text{ft}$

Picture...https://static.k12.com/nextgen_media/assets/8107326-NG_GMT_DP024_232_014.jpg

5. What is m∠V ?

Round only your final answer to the nearest tenth.

53.9º

56.1º

61.9º

70.0º

$\begin{array}{|rcll|} \hline 7.4^2 &=& 8.6^2+7.6^2-2\cdot 8.6\cdot 7.6\cdot \cos(V) \\ 54.76 &=& 73.96 + 57.76 -130.72\cdot \cos(V) \\ 54.76 &=& 131.72 -130.72\cdot \cos(V) \\ 130.72\cdot \cos(V) &=& 131.72 - 54.76 \\ 130.72\cdot \cos(V) &=& 76.96 \\\\ \cos(V) &=& \dfrac{76.96}{130.72} \\\\ \cos(V) &=& 0.58873929009 \\ \angle{V} &=& 53.9324046479^{\circ} \\ \hline \end{array}$

$\angle{V} = 53.9^{\circ}$