Question

A vertical pole, of height b, casts a shadow onto the ground. The angle of elevation from the tip of the shadow on the ground to the top of the pole is θ=30∘, and the distance between the top of the pole and the tip of the shadow is 95 feet. Use the dimensions given to find the height b, in feet, of the pole. Do not include the units in your answer. Type your answer as a decimal.

Answer 1

Answer: $b=47.5$

Step-by-step explanation:

Draw a Rigth triangle as the one attached, where "b" is the height in feet of the pole.

IFor this exercise you need to use the following Trigonometric Identity:

$sin\theta=\frac{opposite}{hypotenuse}$

In this case, you can identify that:

$\theta=30\°\\\\opposite=b\\\\hypotenuse=95$

Then, knowing these values, you can substitute them into $sin\theta=\frac{opposite}{hypotenuse}$, as below:

$sin(30\°)=\frac{b}{95}$

Finally, you must solve for "b" in order to find its value. You get that this is:

$95*sin(30\°)=b\\\\b=47.5$