Question

NO LINKS!! URGENT HELP PLEASE!!!

Draw and label a diagram, then solve for the missing part. Round to the nearest tenth.
Please help me with #7 and 8

Answer 1

7) The buildings are 193.2 feet apart (nearest tenth).

8) The horizontal distance between Zack and the water fountain is 141.1 feet (nearest tenth).

Explanation:

Question 7

See attachment 1 for the diagram that models the given scenario.

We need to find the distance between the two buildings, marked as "x" on the attached diagram.

Given Building B is 654 feet tall and Building A is 480 feet, the different in height is:

`\implies 654-480=174`

Therefore, Building B is 174 ft taller than Building A.

Therefore, we have a right triangle where the angle is 42°, the side opposite the angle measures 174 ft and the side adjacent the angle is x.

This means we can use the tangent trigonometric ratio to calculate x.

`\boxed{\begin{minipage}{6 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}`

Substitute the values into the ratio and solve for x:

`\implies \tan 42^(\circ)=(174)/(x)`

`\implies x=(174)/(\tan 42^(\circ))`

`\implies x=193.246577...`

`\implies x=193.2\sf\;ft\;(nearest\;tenth)`

Therefore, the buildings are 193.2 feet apart (to the nearest tenth).

Question 8

We can model the given scenario as a right triangle (see attachment 2).

We need to find the horizontal distance between the lookout tower and the fountain, marked as "y" on the attached diagram.

As we have a right triangle where the angle is 28°, the side opposite the angle measures 75 ft and the side adjacent the angle is y, this means we can use the tangent trigonometric ratio to calculate y.

`\boxed{\begin{minipage}{6 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}`

Substitute the values into the ratio and solve for y:

`\implies \tan 28^(\circ)=(75)/(y)`

`\implies y=(75)/(\tan 28^(\circ))`

`\implies x=141.054484...`

`\implies x=141.1\sf\;ft\;(nearest\;tenth)`

Therefore, the horizontal distance between Zack and the water fountain is 141.1 feet (nearest tenth).