Dr. Black is standing 15 feet away from the street lamp. The lamp is making his shadow 8 feet long. The angle of elevation from the tip of the shadow to the tip of the streetlamp is 50 degrees. How tall is the streetlamp?

its actually 27

If I am understanding this picture,

a right triangle is formed with angle A = 50 degrees and side b = 23 (15 + 8).

You need the length of a, which is the streetlamp.

tan A = opp/adj = a/b = a/23
tan 50 = a/23
1.19 = a/23

Solve for a, for your answer

27.37

20 To determine the height of the streetlamp, we can use trigonometric functions, specifically tangent.

Let's denote the height of the streetlamp as "h".

From the given information, we have:

- Distance from Dr. Black to the streetlamp (adjacent side of the angle): 15 feet.
- Length of Dr. Black's shadow (opposite side of the angle): 8 feet.
- Angle of elevation from the tip of the shadow to the tip of the streetlamp: 50 degrees.

We can find the tangent of this angle by dividing the length of the opposite side (shadow) by the length of the adjacent side (distance from Dr. Black to the streetlamp).

Tangent (θ) = Opposite / Adjacent = 8 / 15

Using a calculator, we can find that tan(50 degrees) is approximately 1.1918.

1.1918 = 8 / 15 (simplifying the tangent expression)

To solve for the height of the streetlamp (h), we can rearrange the equation:

h = 15 * 1.1918

Calculating the value, we find that the height of the streetlamp is approximately 17.877 feet.