# A Tree Application

#### xyz_1965

##### Member
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
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.

Last edited:

#### xyz_1965

##### Member
see above $\color{red}\text{comments}$ in the quote.
Thank you for correcting my typos.

#### Klaas van Aarsen

##### MHB Seeker
Staff member
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".

#### xyz_1965

##### Member
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.