Find the Tangent Given the Point (9,40)

Problem

(9,40)

Solution

1. Identify the coordinates of the given point (x,y) where x=9 and y=40

2. Determine the radius r of the circle passing through the origin and the point (9,40) using the Pythagorean theorem r=√(,x2+y2)

r=√(,9+40)

r=√(,81+1600)

r=√(,1681)

r=41

3. Apply the formula for the tangent trigonometric function, which is defined as the ratio of the y-coordinate to the x-coordinate.

tan(θ)=y/x

4. Substitute the values x=9 and y=40 into the formula.

tan(θ)=40/9

Final Answer

tan(θ)=40/9

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