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lina2011 [118]
3 years ago
10

What is 0.25(2d+1)... I need help...

Mathematics
1 answer:
IRISSAK [1]3 years ago
6 0
Solution:

1) Distribute
0.25\times 2d+0.25

2) Simplify 0.25\times 2d to (0.5)d
0.5d+0.25

Done!
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A hot air balloon is flying at an altitude of 800 feet. A passenger takes a picture of the top of a tree and estimates that the
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The height of the tree given the depression angle to the top and the base

is given by the tangent relationship of the two given angles.

Correct response:

  • The height of the tree is approximately <u>79.58 feet</u>
<h3 /><h3>Methods used for the calculation of the height of the tree</h3>

Given:

Altitude of the hot air balloon = 800 feet

Angle of depression to top of tree = 43°

Angle of depression to base of tree = 46°

Required:

Height of tree

Solution:

The horizontal distance of the balloon from the tree is given as follows;

  • \displaystyle tan(46^{\circ}) = \frac{Altitude \ of \ balloon}{Horizontal \ distance \ from \ tree} = \mathbf{\frac{800 \, feet}{Horizontal \ distance \ from \ tree}}

Therefore;

\displaystyle Horizontal \ distance \ of \ balloon \  from \ tree = \frac{800 \ feet}{tan(46^{\circ})}

  • \displaystyle tan(43^{\circ})  = \mathbf{\frac{Height \ of \ balloon \ above \ tree}{\dfrac{800 \, feet}{tan(46^{\circ})} }}

Therefore;

\displaystyle Height \ of \ balloon \ above \ tree = tan(43^{\circ}) \times \frac{800 \, feet}{tan(46^{\circ})}

  • Height of tree = Altitude of balloon - Height of balloon above tree

Therefore;

  • \displaystyle Height \ of \ tree = 800 \, feet - tan(43^{\circ}) \times \frac{800 \, feet}{tan(46^{\circ})} \approx \underline{  79.58 \, feet}

Learn more about angle of elevation and depression here:

brainly.com/question/1978238

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