Dr. Black is standing 20 feet from a streetlamp. The lamp is making his shadow 5 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 30 degrees. To the nearest foot, the streetlamp is about _____.
Did you make your sketch?
I will assume you want the height of the streetlamp?
then tan30° = height/25
continue ....
14
14.43
To find the height of the streetlamp, we can use the tangent function. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
Let's call the height of the streetlamp "h". The opposite side is 5 feet (Dr. Black's shadow) and the adjacent side is 20 feet (the distance between Dr. Black and the streetlamp). We can set up the equation:
tan(30°) = height of the streetlamp / distance from Dr. Black to the streetlamp
Now we can solve for the height of the streetlamp:
tan(30°) = h / 20
To find the value of the tangent of 30 degrees, refer to a trigonometric table or use a calculator. The tangent of 30 degrees is approximately 0.5774.
0.5774 = h / 20
To find the height of the streetlamp, multiply both sides of the equation by 20:
20 * 0.5774 = h
11.548 = h
Rounding to the nearest foot, the height of the streetlamp is approximately 12 feet.
Therefore, the streetlamp is about 12 feet tall.