Find the Tangent Given the Point (10,24)

Problem

(10,24)

Solution

1. Identify the coordinates of the given point (x,y) where x=10 and y=24

2. Determine the radius r of the circle passing through the origin and this point using the Pythagorean theorem r=√(,x2+y2)

3. Calculate the radius value: r=√(,10+24)=√(,100+576)=√(,676)=26

4. Apply the trigonometric definition for the tangent function, which is the ratio of the y-coordinate to the x-coordinate.

5. Substitute the values into the formula tan(θ)=y/x

6. Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

Final Answer

tan(θ)=12/5

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