A 20-meter line is used to tether a helium-filled balloon.Because of a breeze, the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity.
A) $\sin 85 ^ { \circ } = \frac { h } { 20 }$ (where h is height.)
B) $\cos 85 ^ { \circ } = \frac { h } { 20 }$ (where h is height.)
C) $\cos 85 ^ { \circ } = \frac { 20 } { h }$ (where h is height.)
D) $\sin 85 ^ { \circ } = \frac { 20 } { h }$ (where h is height.)
E) $\tan 85 ^ { \circ } = \frac { h } { 20 }$ (where h is height.)

Question

A 20-meter line is used to tether a helium-filled balloon.Because of a breeze, the line makes an angle of approximately 85° with the ground.Use a trigonometric function to write an equation involving the unknown quantity.  
A) $\sin 85 ^ { \circ } = \frac { h } { 20 }$ (where h is height.)
B) $\cos 85 ^ { \circ } = \frac { h } { 20 }$ (where h is height.)
C) $\cos 85 ^ { \circ } = \frac { 20 } { h }$ (where h is height.)
D) $\sin 85 ^ { \circ } = \frac { 20 } { h }$ (where h is height.)
E) $\tan 85 ^ { \circ } = \frac { h } { 20 }$ (where h is height.)

Quizplus · Accepted Answer

The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. Here, $h$ is the opposite side (height of the balloon) and 20 meters is the hypotenuse (length of the line).

A 20-Meter Line Is Used to Tether a Helium-Filled Balloon sin⁡85∘=h20\sin 85 ^ { \circ } = \frac { h } { 20 }sin85∘=20h​

A 20-Meter Line Is Used to Tether a Helium-Filled Balloon $\sin 85 ^ { \circ } = \frac { h } { 20 }$