Calvin Butterball is lying on the ground and spots a hot air balloon at an angle of elevation of 28 The distance from Calvin to the hot air balloon is 850 feet. How high in the air is the balloon?

 approximately 399 feet

The more accurate value is 399.050828368008 feet, but this value is still approximate.

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Work Shown:

Refer to the diagram below.

To find x, we'll use the sine rule

sin(angle) = opposite/hypotenuse

sin(28) = x/850

850*sin(28) = x

x = 850*sin(28)

x = 399.050828368008 ...... make sure your calc is in degree mode

x = 399

I'm rounding to the nearest whole number since the given values (28 and 850) are also whole numbers. If your teacher provides other rounding instructions, then be sure to follow that.

The hot air balloon is approximately 399 feet off the ground.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!