Question

The angle looking up at the sun is 70°. A flagpole casts a shadow of 15 ft. Draw a diagram and find the height of the flagpole

Answer 1

Answer:

Option A is correct

the height of the flagpole is, 41.2 ft

Step-by-step explanation:

As per the statement:

The angle looking up at the sun is 70°

⇒$\theta= 70^{\circ}$

It is also given that:

A flagpole casts a shadow of 15 ft.

For this you can see the diagram as shown below in the attachment.

Now, find the height of the flagpole.

Let h be the height of flagpole.

using tangent ratio:

$\tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}}$

From the given diagram;

$\theta = 70^{\circ}$

Opposite side = Height of the Flag pole = h

Adjacent  side = Shadow of the flagpole = 15 ft

Substitute these we get;

$\tan 70^{\circ} = \frac{h}{15}$

Multiply both sides by 15 we get;

$15 \cdot \tan 70^{\circ} = h$

$15 \cdot 2.75 = h$

Simplify:

$41.2 ft = h$

or

h = 41.2 ft

Therefore, the height of the flagpole is, 41.2 ft

Answer 2

Answer:

The length of the flagpole be 41.2 ft .

Option (A) is correct .

Step-by-step explanation:

As given

The angle looking up at the sun is 70°.

A flagpole casts a shadow of 15 ft .

Now by using the trignometric identity .

$tan \theta = \frac{Perpendicular}{Base}$

$\ theta = 70^{\circ}$

$tan\ 70^{\circ} = \frac{AB}{BC}$

BC = 15 ft

tan 70° = 2.75 (Approx)

$2.75 = \frac{AB}{15}$

AB = 2.75 × 15

     = 41.2 ft

Therefore the length of the flagpole be 41.2 ft .

Option (A) is correct .