A 10-meter line is used to tether a helium-filled balloon.Complete the table,which shows the heights (in meters)of the balloon for decreasing angle measures $\theta$ .(Round your answers to one decimal places. ) $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & & & & & \
\hline
\end{array}$$
A) $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 5.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Angle } , \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 7.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 4.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 3.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 6.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$

Question

A 10-meter line is used to tether a helium-filled balloon.Complete the table,which shows the heights (in meters)of the balloon for decreasing angle measures $\theta$ .(Round your answers to one decimal places. ) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & & & & & \
\hline
\end{array}$$
A) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 5.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle } , \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 7.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 4.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 3.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Angle, } \theta & 50 ^ { \circ } & 40 ^ { \circ } & 30 ^ { \circ } & 20 ^ { \circ } & 10 ^ { \circ } \
\hline \text { Height } & 6.7 & 6.4 & 5 & 3.4 & 1.7 \
\hline
\end{array}$$

Quizplus · Accepted Answer

To find the height of the balloon, we use the sine function in trigonometry because the height forms the opposite side of the right triangle, the tether line is the hypotenuse, and the angle $\theta$ is given. The formula is $\text{height} = \text{hypotenuse} \times \sin(\theta)$. For a 10-meter line:- At $50^\circ$, $\text{height} = 10 \times \sin(50^\circ) \approx 7.7$ meters.- At $40^\circ$, $\text{height} = 10 \times \sin(40^\circ) \approx 6.4$ meters.- At $30^\circ$, $\text{height} = 10 \times \sin(30^\circ) = 5$ meters (since $\sin(30^\circ) = 0.5$).- At $20^\circ$, $\text{height} = 10 \times \sin(20^\circ) \approx 3.4$ meters.- At $10^\circ$, $\text{height} = 10 \times \sin(10^\circ) \approx 1.7$ meters.

A 10-Meter Line Is Used to Tether a Helium-Filled Balloon θ\thetaθ

A 10-Meter Line Is Used to Tether a Helium-Filled Balloon $\theta$