A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges at an angle of 6.2×10−5 rad. What diameter spot will it make on the Moon?

Express your answer using two significant figures.

diameter= angle*distance= 6.2E-5*380000km=23km check that.

Initially I got 2356000 and I made that 2.4 x 10^6 because they wanted two significant figures but that was incorrect. I tried your answer and that is also not right. What am I doing wrong here? Please helP!

23.6 km or 23,600 meters looks right to me.

To find the diameter spot that the laser beam will make on the Moon, we can use the formula for calculating the diameter of the spot, which is given by the following equation:

Δd = 2 * D * tan(θ/2)

Where:
Δd is the diameter of the spot on the Moon,
D is the distance from Earth to the Moon (380,000 km), and
θ is the angle at which the laser beam diverges (6.2×10^(-5) rad).

Now let's substitute the given values into the formula and solve for Δd:

Δd = 2 * (380,000 km) * tan(6.2×10^(-5)/2)

First, convert the distance from kilometers to meters:
Δd = 2 * (380,000 km * 1000 m/km) * tan(6.2×10^(-5)/2)

Next, calculate the value within the tangent function:
Δd = 2 * (380,000 km * 1000 m/km) * tan(6.2×10^(-5)/2)
Δd = 2 * 380,000,000 m * tan(6.2×10^(-5)/2)

Now calculate the tangent of half the angle:
Δd = 2 * 380,000,000 m * tan(6.2×10^(-5)/2)
Δd = 2 * 380,000,000 m * tan(3.1×10^(-5))

Finally, we can calculate the diameter of the spot using a calculator:

Δd ≈ 2 * (380,000,000) * tan(3.1×10^(-5))
Δd ≈ 2 * (380,000,000) * 3.1×10^(-5)
Δd ≈ 23,540

Therefore, the diameter of the spot that the laser beam will make on the Moon is approximately 23,540 meters.