altitude 1208 m, angle of depr. 17 deg; find ground distance

[maria1983]

1) A ballonist records his altitude as 1208 meters. At the same time, his partner measures the angle of depression from their location to their landing spot to be 17 degrees. How far away, correct to the nearest meter, is the landing spot from a point on the ground directly below the balloon?

[jaybird0827]

1) A ballonist records his altitude as 1208 meters. At the same time, his partner measures the angle of depression from their location to their landing spot to be 17 degrees. How far away, correct to the nearest meter, is the landing spot from a point on the ground directly below the balloon?

Where are you stuck? Please show what you've done so far to attempt to solve the problem. Thank you!

[stapel_eliz]

1) A ballonist records his altitude as 1208 meters. At the same time, his partner measures the angle of depression from their location to their landing spot to be 17 degrees. How far away, correct to the nearest meter, is the landing spot from a point on the ground directly below the balloon?

Draw a right triangle, with the base being the ground distance, the altitude being the balloon's altitude, and the hypotenuse being the line of sight. Label the height line as "1208" and the angle at the landing site as "17 degrees". Label the base as "d", being the distance you need to find.

Now consider the triangle and the trig ratios, and use one of those ratios to find the required value.