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: $7\ feet$

Step-by-step explanation:

You need to analize the picture attached.

You can use the following Trigonometry Identity:

$tan\alpha =\frac{opposite}{adjacent}$

 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  $tan\alpha =\frac{opposite}{adjacent}$ and solve for "h" in order to find its value.

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

$tan(16.3\°)=\frac{h}{24}\\\\24*tan(16.3\°)=h\\\\h\approx7$