Respuesta :

Find height:

[tex]\boxed {\boxed { \sin(\theta) = \dfrac{\text{opp}}{\text{hyp}} }}[/tex]

[tex]\sin(60) = \dfrac{\text{opp}}{8}} [/tex]

[tex]\text{opp} = 8\sin(60) [/tex]

[tex]\text{opp} = 6.93 \text{ ft}[/tex]

Height = 6.93

Find missing base length:

[tex]\boxed { \boxed { \cos(\theta) = \dfrac{\text{adj}}{\text{hyp}} }}[/tex]

[tex]\cos(60) = \dfrac{\text{adj}}{8}} [/tex]

[tex]\text{adj} = 8\cos(60) [/tex]

[tex]\text{adj} = 4 \text{ ft}[/tex]

Base length = 7 + 4 = 11 ft

Find area:

[tex]\boxed {\boxed { \text {Area of trapezium = } \dfrac{1}{2} (a + b)h}}[/tex]

[tex]\text {Area of trapezium = } \dfrac{1}{2} (11 +7)(6.93)[/tex]

[tex]\text {Area of trapezium = } 62.4 \text{ ft. (nearest tenth)}[/tex]

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