Question

GEOMETRY PLEASE HELP!! for 30 points!

Looking up, Joe sees two hot air balloons in the sky as shown. He determines that the hot air balloon is 700 meters away, at an angle of 38 degrees from the vertical. The higher hot air balloon is 1,050 meters away, at an angle of 26 degrees from the vertical. How much higher is the balloon on the right than the balloon on the left?

Do not round any intermediate computations. Round your answer to the nearest tenth.

Note that the figure below is not drawn to scale.

Answer 1

Sure, I can help you with that. Here are the steps on how to solve the problem:

1. Let x be the height of the balloon on the left and y be the height of the balloon on the right.

2. Using the tangent function, we can write the following equations:

```

tan(38) = x/700

tan(26) = y/1050

```

3. Solve the first equation for x:

```

x = 700tan(38)

```

4. Substitute this value of x into the second equation:

```

y/1050 = tan(26)

y = 1050tan(26)

```

5. Subtract the two equations to find the difference between the heights of the two balloons:

```

y - x = 1050tan(26) - 700tan(38)

```

6. Evaluate this expression using a calculator and round your answer to the nearest tenth:

```

y - x = 266.51 meters

```

Therefore, the balloon on the right is 266.51 meters higher than the balloon on the left.

Explanation:

Answer 2

To find the difference in height between the two hot air balloons, we need to find the heights of each balloon first.

Let's call the height of the balloon on the left "h1" and the height of the balloon on the right "h2".

Using trigonometry, we can find the height of each balloon as follows:

tan(38) = h1/700
h1 = 700 tan(38) = 524.1 m

tan(26) = h2/1050
h2 = 1050 tan(26) = 479.7 m

The difference in height between the two balloons is:

h2 - h1 = 479.7 - 524.1 = -44.4 m

Since the answer is asking for the difference in height, and the balloon on the right is lower than the one on the left, the answer is negative.

Rounding to the nearest tenth, we get:

The balloon on the right is 44.4 meters lower than the balloon on the left.

Therefore, the answer is "-44.4 meters."