Question

Find y on this special right triangle

Answer 1

• Cos(x) = adjacent side/hypotenuse

`cos(45)=((7√(2) )/(2) )/(x) \\\\cos(45)x=(7√(2) )/(2)\\\\(√(2) )/(2)x=(7√(2) )/(2)\\\\x=((7√(2) )/(2))/((√(2) )/(2)) =(7√(2) )/(2)*(2)/(√(2)) =7`

• Use the Pythagorean Theorem to find y

`y^(2) +((7√(2) )/(2) )^(2) =x^(2) \\\\y^(2) =7^(2)-((7√(2) )/(2) )^(2) \\\\y^(2)=49-(49(2))/(4) =49-(49)/(2)=(49(2))/(2)-(49)/(2)=(98-49)/(2)=(49)/(2) \\\\y=\sqrt{(49)/(2) } =(7)/(√(2) ) =(7√(2))/(√(2)(√(2))) =(7√(2))/(2)`