Question

Artemis seeks knowledge of the width of Orion's Belt, which is a pattern of stars in the Orion constellation. She has previously discovered the distances from her house to Alnitak (736(736left parenthesis, 736 light years, \text{l.Y.})l.Y.)start text, l, point, y, point, end text, right parenthesis and to Mintaka (915\text{ l.Y.})(915 l.Y.)left parenthesis, 915, start text, space, l, point, y, point, end text, right parenthesis, which are the endpoints of Orion's Belt. She also knows the angle between these stars in the sky is 3^\circ3 ∘ 3, degrees. What is the width of Orion's Belt? That is, what is the distance between Alnitak and Mintaka? Do not round during your calculations. Round your final answer to the nearest light year.

Answer 1

Answer:

Orion's belt width is 184 light years

Step-by-step explanation:

So we want to find the distance between Alnitak and Mintaka, which is the Orions belts

Let the distance between the Alnitak and Mintaka be x,

Then applying cosine

c²=a²+b²—2•a•b•Cosθ

The triangle is formed by the 736 light-years and 915 light years

Artemis from Alnitak is

a = 736lightyear

Artemis from Mintaka is

b = 915 light year

The angle between Alnitak and Mintaka is θ=3°

Then,

Applying the cosine rule

c²=a²+b²—2•a•b•Cosθ

c² =736² + 915² - 2×, 736×915×Cos3

c² = 541,696 + 837,225 - 1,345,034.1477702404

c² = 33,886.85222975954

c = √33,886.85222975954

c = 184.0838184897 light years

c = 184.08 light years

So, to the nearest light year, Orion's belt width is 184 light years