Question

The angles of elevation of a hot air balloon from the two points on level ground are 20° and 42° respectively. If the points are 4.8 miles apart and the balloon is between the points, approximate, to the nearest tenth of a mile, the height of the balloon above the ground.

Answer 1

on usatestprep its 1.2

Explanation:

Answer 2

To the nearest tenth, the height of the balloon is 2.9 miles

Explanation:

The nearer point takes the greater angle of elevation.

The diagram is shown in the attachment.

The height of the balloon above the ground is c unit.

From triangle ABD,

`\tan 42\degree=(c)/(x)`

`\implies x=(c)/(\tan 42\degree)`...eqn1

From triangle ABC,

`\tan 20\degree=(c)/(x+4.8)`

`\implies x+4.8=(c)/(\tan 20\degree)`

`\implies x=(c)/(\tan 20\degree)-4.8`..eqn2

We equate both equations and solve for c.

`(c)/(\tan 42\degree)=(c)/(\tan 20\degree)-4.8`

`(c)/(\tan 42\degree)-(c)/(\tan 20\degree)=-4.8`

`\implies ((1)/(\tan 42\degree)-(1)/(\tan 20\degree))c=-4.8`

`\implies -1.636864905c=-4.8`

`\implies c=(-4.8)/(-1.636864905)`

`c=2.932435039`

To the nearest tenth, the height of the balloon is 2.9 miles