Pre calc question patty is 50 mi. due north of todd. emma is due east of todd. if a line were drawn from emma to todd and from emma to patty, the angle formed would measure 40 degrees. to the nearest mile, how far is emma from each person?

Answers:

1) Distance from Emma to Patty: 77.8 miles

2) Distance from Emma to Todd: 59.6 miles

Procedure:

You can trace a nice right triangle with the information given.

I have drawn it and attached in case you need a visualization help. Open the attached.

This is the solution, step-by-step:

1) The distance from Todd to Emma, 50 miles, is the oppositte-leg to the 40° angle.

2) Y, the distance from Emma to Patty, is the hypotenuse of the triangle.

3) X, the distance from Emma to Todd, is the adjacent-leg to the 40° angle.

4) With that information you can use the trigonometric ratios to find your unknowns:

4.1) sin(40°) = opposite-leg / hypotenuse = 50 / Y => Y = 50 / sin(40°)

Y = 77.8 miles

4.2) tan (40°) = opposite-leg / adjacent-leg= 50 / X => X = 50 / tan(40°)

X = 59.6 miles

The length of what is left would be 1 1/2 feet long.