Answer:
j = 19.6
k = 25.9
J = 49°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.
<h3>Analysis</h3>
The given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Tan = Opposite/Adjacent ⇒ Adjacent = Opposite/Tan
Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.
<h3>Application</h3>
Hypotenuse = Opposite/Sin
IJ = 17/sin(41°) ≈ 25.9
Adjacent = Opposite/Tan
IK = 17/tan(41°) ≈ 19.6
Angle J = 90° -41° = 49°
In summary, ...
j = 19.6
k = 25.9
J = 49°
Answer:
x = 2±sqrt(11)
Step-by-step explanation:
x^2 -4x - 7 =0
Add 7 to each side
x^2 -4x -7+7 =0+7
x^2 -4x =7
To complete the square take the coefficient of the x term and divide by 2 and then square it. Add it to both sides
-4 /2 = -2 then square
(-2)^2 = 4
Add 4 to both sides
x^2 -4x+4 =7+4
x^2 -4x+4 = 11
Factor the left side into (x-b/2)^2
(x-2)^2 =11
Take the square root of each side
sqrt((x-2)^2) =±sqrt(11)
x-2 = ±sqrt(11)
Add to to each side
x-2+2 = 2±sqrt(11)
x = 2±sqrt(11)
