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.
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.
Solution Summary: The author explains how to graph a right-angled triangle with known sides and the height of the balloon.
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.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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