Math  /  Geometry

QuestionThe point (10,22)(-10,22) is on the terminal side of the angle and x=10,y=22x=-10, y=22. First find the value of rr. r=x2+y2=+484=\begin{aligned} r & =\sqrt{x^{2}+y^{2}} \\ & =\sqrt{ }+484 \\ & =\sqrt{ } \end{aligned}

Studdy Solution

STEP 1

1. The point (10,22)(-10, 22) is given on the terminal side of an angle in standard position.
2. The coordinates of the point are x=10x = -10 and y=22y = 22.
3. The value of rr is defined as the distance from the origin to the point (x,y)(x, y), which can be found using the Pythagorean theorem.
4. The formula for rr is r=x2+y2r = \sqrt{x^2 + y^2}.

STEP 2

1. Substitute the values of xx and yy into the formula for rr.
2. Calculate x2x^2 and y2y^2.
3. Add the results of x2x^2 and y2y^2.
4. Take the square root of the sum to find rr.

STEP 3

Substitute the given values of xx and yy into the formula for rr.
r=(10)2+222 r = \sqrt{(-10)^2 + 22^2}

STEP 4

Calculate x2x^2.
x2=(10)2=100 x^2 = (-10)^2 = 100

STEP 5

Calculate y2y^2.
y2=222=484 y^2 = 22^2 = 484

STEP 6

Add x2x^2 and y2y^2.
x2+y2=100+484=584 x^2 + y^2 = 100 + 484 = 584

STEP 7

Take the square root of the sum to find rr.
r=584 r = \sqrt{584}
Solution: The value of rr is 584\sqrt{584}, which simplifies to 21462\sqrt{146}.

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