A 20-meter line is used to tether a helium-filled balloon. The line makes an angle of approximately 85° with the ground because of a breeze.
(a) Draw a right triangle that gives a visual representation of the problem. Label the known quantities of the triangle and use a variable to represent the height of the balloon.
(b) Use a trigonometric function to write and solve an equation for the height of the balloon.
(c) The breeze becomes stronger and the angle the line makes with the ground decreases. How does this affect the triangle you drew in part(a)?
(d) Complete the table, which shows the heights (in meters) of the balloon for decreasing angle
measures θ.

(e) As θ approaches 0°, how does this affect the height of the balloon? Draw a right triangle to explain your reasoning.

Transcribed Image Text:

Angle, 0 60° 80° 70° 50° Height 20° 10° Angle, 0 40° 30° Height