A hunter on top of a tower sees a fire at an angle of depression of 30⁰. The height of the tower is 18m. What is the distance between the fire and the hunter. Round of your answer to 2SF
Let x be the distance between the fire and the hunter.
Using trigonometry, we know that tan(30⁰) = 18 / x.
Therefore, x = 18 / tan(30⁰).
Using a scientific calculator, tan(30⁰) is approximately 0.5774.
Thus, x = 18 / 0.5774 = 31.1632.
Rounded to 2 significant figures, the distance between the fire and the hunter is 31 m.
To find the distance between the fire and the hunter, we need to use trigonometry.
Let's assume that the distance between the fire and the hunter is represented by the variable "x".
In this scenario, the angle of depression is given as 30⁰, which means that the angle formed between the horizontal line and the line of sight from the hunter to the fire is 30⁰.
Since we have a right-angled triangle formed by the hunter, the tower, and the line of sight to the fire, we can use the tangent function.
We can use the tangent function to write an equation:
tan(30⁰) = opposite/adjacent
tan(30⁰) = x/18m
To solve for x, we'll rearrange the equation:
x = 18m * tan(30⁰)
Using a calculator, tan(30⁰) = 0.5773 (rounded to 4 decimal places).
x ≈ 18m * 0.5773
x ≈ 10.39m
Therefore, the distance between the fire and the hunter is approximately 10.39m (rounded to 2 significant figures).