Answer:
A. You can not use the Pythagorean theorem because you would need the length of at least two sides but the triangle only provides the length of one.
B. x ≈ 7 ft. y ≈ 6 ft.
Step-by-step explanation:
Sin(51) = [tex]\frac{x}{9}[/tex]
Sin(51)*9 = x
x = 6.99431
x ≈ 7 ft.
Now you can use the Pythagorean theorem.
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]7^{2} +b^{2} =9^{2}[/tex]
[tex]49+b^{2} =81[/tex]
[tex]b^{2}[/tex] = 32
[tex]\sqrt{b^{2} } =\sqrt{32}[/tex]
b = 5.65685
y ≈ 6 ft.
Or, continue to use the cosine.
Cos(51) = [tex]\frac{y}{9}[/tex]
Cos(51)*9 = y
y = 5.66388
y ≈ 6 ft.
Answer Check
We know c = 9 ft.
[tex]a^{2}+ b^{2}= c^{2} \\7^{2}+ 6^{2}= c^{2}\\49+36=c^{2}\\ 85 = c^{2} \\\sqrt{85} =\sqrt{c^{2} } \\c=9.21954\\c=9 ft.[/tex]
