Question

The angle subtended by moon at a point on earth is 31'. If the distance of moon from earth is 3.34 x 10^8 m, find the diameter of the moon.​

Answer 1

Answer:

The diameter will be approximately 3000 km.

Explanation:

The formula for angular size is:

δ = 2 arc sin(d/2D)

Here,

• δ  is the angular size

• d is the diameter of the object (in this case the Moon

• D is the distance.

We can rearrange the formula to:

• d = 2D sin(δ/2)
• δ = 31′ ≈ 0.5167
• D = 3.34×10⁸ m  

If we plug in the values:

⇒ d ≈ 2 ×3.34 × 10⁸ × sin(0.5167/2)

⇒ d ≈ 6.68 × 10⁸ × sin(0.2583)  

⇒ d ≈ 6.68 × 10⁸ × 0.0045

⇒ d ≈ 3011846 m

⇒ d ≈ 3011.846 km

⇒ d ≈ 3000 kilometres

So, the diameter will be approximately 3000 km.