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Crazy boy [7]
3 years ago
10

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 th

e nearest inch?

Mathematics
1 answer:
Makovka662 [10]3 years ago
8 0

Answer:

The height of Sandy is 68.74 inches.

Step-by-step 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 =\frac{perpendicular}{base}

In triangle ABC,

\tan(\angle C)=\frac{AB}{BC}

\tan(32^{\circ})=\frac{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.

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