Question

a closed umbrella casts a shadow when the sun shines at a 16.3-degree angle to the ground. how tall is the top of the umbrella to the nearest foot ?

Answer 1

Answer:
`7\ feet`

Explanation:

You need to analize the picture attached.

You can use the following Trigonometry Identity:

`tan\alpha =(opposite)/(adjacent)`

Let call "h" the height in feet of the umbrella.

In this case you can identify that:

`\alpha =16.3\°\\\\opposite=h\\\\adjacent=24`

Therefore, kwnowing these values you can substitute them into
`tan\alpha =(opposite)/(adjacent)` and solve for "h" in order to find its value.

Applying this procedure, you get that the height of this umbrella is:

`tan(16.3\°)=(h)/(24)\\\\24*tan(16.3\°)=h\\\\h\approx7`