Question

When the sun has risen 32 degrees above the horizon, Sandy casts a shadow that is 9 feet 2 inches long. How tall is Sandy, to the nearest inch?

Answer 1

The height of Sandy is 68.74 inches.

Explanation:

It is given that the sun has risen 32 degrees above the horizon. It means the angle of elevation is 32°.

Let the height of Sandy be x.

Sandy casts a shadow that is 9 feet 2 inches long.

We know that 1 feet = 12 inches

Using this conversion, we get

Shadow = 9 feet 2 inches = 9(12)+2 = 110 inches

In a right angled triangle,

`\tan\theta =(perpendicular)/(base)`

In triangle ABC,

`\tan(\angle C)=(AB)/(BC)`

`\tan(32^(\circ))=(x)/(110)`

Multiply both sides by 110.

`110\tan(32^(\circ))=x`

`68.73562871=x`

`x\approx 68.74`

Therefore the height of Sandy is 68.74 inches.