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Andrej [43]
3 years ago
9

The sun is 24 degreesabove the horizon. It makes a 51 m long shadow of a tall tree. how talll is the tree

Mathematics
1 answer:
Advocard [28]3 years ago
8 0

Answer:

The tree is approximately 22.707 meters tall.

Step-by-step explanation:

The geometric diagram of the problem is included below as attachment. The height of the tree is found by means of trigonometric functions:

\tan \alpha = \frac{h}{w}

Where:

\alpha - Elevation angle, measured in sexagesimal degrees.

h - Height of the tree, measured in meters.

w - Length of the tree shadow, measured in meters.

The height of the tree is cleared in the equation:

h = w\cdot \tan \alpha

If w = 51\,m and \alpha = 24^{\circ}, the height is:

h = (51\,m)\cdot \tan 24^{\circ}

h \approx 22.707\m

The tree is approximately 22.707 meters tall.

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Step-by-step explanation:

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