A right triangle is shown. Which is closest to the value of x?

option D is correct

Step-by-step explanation:

The given figure is a right angle triangle.

From the given right angle triangle,

the hypotenuse of the right angle triangle is 15

With 22° as the reference angle,

the adjacent side of the right angle triangle is the unknown side.

the opposite side of the right angle triangle is x.

To determine x, we would apply

the sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore,

Sin 22 = x/15

x = 15Sin22 = 15 × 0.3746

x = 5.6 to the nearest tenth.

the answer is 2 + i.

Step-by-step explanation:

Let the square root of 3 + 4i be x + iy.

So (x + iy) (x +iy) = 3 +4i

=> x^2 + xyi + xyi + i^2*y^2 = 3 + 4i

=> x^2 – y^2 + 2xyi = 3 + 4i

Equate the real and complex terms

=> x^2 - y^2 = 3 and 2xy = 4

2xy = 4

=> xy = 2

=> x = 2/y

Substitute in

=> x^2 - y^2 = 3

=> 4/y^2 - y^2 = 3

=> 4 – y^4 = 3y^2

=> y^4 + 3y^2 – 4 = 0

=> y^4 + 4y^2 – y^2 – 4 =0

=> y^2(y^2 + 4) – 1(y^2 + 4) =0

=> (y^2 – 1) (y^2 + 4) =0

Therefore y^2 = 1, we ignore y^2 = -4 as it gives complex values of y.

Therefore y = 1 and x = 2/1 = 2

The required square root of 3 + 4i is 2 + i.