QuestionFind the height of a smokestack that casts a shadow of $1580$ ft when the Sun's angle of elevation is $38^{\circ}$ .

Studdy Solution

STEP 1

Assumptions1. The length of the shadow cast by the smokestack is1580 ft. . The angle of elevation of the Sun is38 degrees.
3. The smokestack, the end of the shadow, and the point where the sun's rays hit the top of the smokestack form a right triangle.

STEP 2

We will use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the smokestack) to the adjacent side (the length of the shadow).
$\tan(\theta) = \frac{Height}{Shadow\, length}$

STEP 3

Now, plug in the given values for the angle of elevation and the shadow length to calculate the height.
$\tan(38^{\circ}) = \frac{Height}{1580\, ft}$

STEP 4

Rearrange the equation to solve for the height.
$Height = \tan(38^{\circ}) \times1580\, ft$

STEP 5

Calculate the height of the smokestack.
$Height = \tan(38^{\circ}) \times1580\, ft \approx1200\, ft$ The smokestack is approximately1200 ft tall.

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QuestionFind the height of a smokestack that casts a shadow of $1580$ ft when the Sun's angle of elevation is $38^{\circ}$ .

Studdy Solution

STEP 1

Assumptions1. The length of the shadow cast by the smokestack is1580 ft. . The angle of elevation of the Sun is38 degrees.
3. The smokestack, the end of the shadow, and the point where the sun's rays hit the top of the smokestack form a right triangle.

STEP 2

We will use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the smokestack) to the adjacent side (the length of the shadow).
$\tan(\theta) = \frac{Height}{Shadow\, length}$

STEP 3

Now, plug in the given values for the angle of elevation and the shadow length to calculate the height.
$\tan(38^{\circ}) = \frac{Height}{1580\, ft}$

STEP 4

Rearrange the equation to solve for the height.
$Height = \tan(38^{\circ}) \times1580\, ft$

STEP 5

Calculate the height of the smokestack.
$Height = \tan(38^{\circ}) \times1580\, ft \approx1200\, ft$ The smokestack is approximately1200 ft tall.

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QuestionFind the height of a smokestack that casts a shadow of 158015801580 ft when the Sun's angle of elevation is 38∘38^{\circ}38∘.

Studdy Solution

STEP 1

Assumptions1. The length of the shadow cast by the smokestack is1580 ft. . The angle of elevation of the Sun is38 degrees.3. The smokestack, the end of the shadow, and the point where the sun's rays hit the top of the smokestack form a right triangle.

STEP 2

We will use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the smokestack) to the adjacent side (the length of the shadow).tan⁡(θ)=HeightShadow length\tan(\theta) = \frac{Height}{Shadow\, length}tan(θ)=ShadowlengthHeight​

STEP 3

Now, plug in the given values for the angle of elevation and the shadow length to calculate the height.tan⁡(38∘)=Height1580 ft\tan(38^{\circ}) = \frac{Height}{1580\, ft}tan(38∘)=1580ftHeight​

STEP 4

Rearrange the equation to solve for the height.Height=tan⁡(38∘)×1580 ftHeight = \tan(38^{\circ}) \times1580\, ftHeight=tan(38∘)×1580ft

STEP 5

Calculate the height of the smokestack.Height=tan⁡(38∘)×1580 ft≈1200 ftHeight = \tan(38^{\circ}) \times1580\, ft \approx1200\, ftHeight=tan(38∘)×1580ft≈1200ftThe smokestack is approximately1200 ft tall.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the height of a smokestack that casts a shadow of $1580$ ft when the Sun's angle of elevation is $38^{\circ}$ .

Assumptions1. The length of the shadow cast by the smokestack is1580 ft. . The angle of elevation of the Sun is38 degrees.
3. The smokestack, the end of the shadow, and the point where the sun's rays hit the top of the smokestack form a right triangle.

We will use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the smokestack) to the adjacent side (the length of the shadow).
$\tan(\theta) = \frac{Height}{Shadow\, length}$

Now, plug in the given values for the angle of elevation and the shadow length to calculate the height.
$\tan(38^{\circ}) = \frac{Height}{1580\, ft}$

Rearrange the equation to solve for the height.
$Height = \tan(38^{\circ}) \times1580\, ft$

Calculate the height of the smokestack.
$Height = \tan(38^{\circ}) \times1580\, ft \approx1200\, ft$ The smokestack is approximately1200 ft tall.