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A Tree Application

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xyz_1965

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Jul 26, 2020
81
A tree casts a 23-foot shadow when the angle of elevation of the sun is 52 degrees.

(A) Find the height of the tree.

(B) Find the length of the shadow when the angle of elevation of the sun is 38 degrees.


Part (A)

Let h = height of tree

tan(52°) = h/52

tan(52°)(23) = h

29.4386575404 = h

Rounding off to the nearest ones place, I get 29 feet.

The tree is 29 feet.

Part (B)

Let s = length of shadow

tan(38°) = 29/s

s = 29/tan(38°)

s = 37.1183073336

After rounding to the nearest unit, I get 37 feet.

The shadow is 37 feet.

Is this right?
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
655
A tree casts a 23-foot shadow when the angle of elevation of the sun is 52 degrees.

(A) Find the height of the tree.

(B) Find the length of the shadow when the angle of elevation of the sun is 38 degrees.


Part (A)

Let h = height of tree.

tan(52°) = h/52

$\color{red} \tan(52) =h/23$

tan(52°)(23) = h

29.4386575404 = h

Rounding off to the nearest ones place, I get 29 feet.

The tree is 29 feet.

Part (B)

Let s = length of shadow

tan(38°) = 29/s

$\color{red} \text{I wouldn’t use the rounded value of the height in subsequent calculations. Final shadow length is closer to 38 ft}$
s = 29/tan(38°)

s = 37.1183073336

After rounding to the nearest unit, I get 37 feet.

The shadow is 37 feet.

Is this right?
see above $\color{red}\text{comments}$ in the quote.
 
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xyz_1965

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Jul 26, 2020
81

Klaas van Aarsen

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Mar 5, 2012
8,736
Thank you for correcting my typos.
It is fine to round a final result, but using a rounded intermediate result for more calculations (in part B) is a bit more serious than a typo. It means that the final result of B will be "off".
 
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xyz_1965

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Jul 26, 2020
81
It is fine to round a final result, but using a rounded intermediate result for more calculations (in part B) is a bit more serious than a typo. It means that the final result of B will be "off".
I'll try to be careful in my rounding off.