An object is 6m away from the base of a mast. The angle of depression of the object from the top of the mast is 50 degree. Find, correct to 2 decimal places, the height of the mast.
h/6 = tan 50°
To find the height of the mast, we can use trigonometry and the concept of angle of depression.
Let's denote the height of the mast as 'h'.
Using the angle of depression, we know that the angle formed between the horizontal line from the top of the mast to the object and the line of sight from the top of the mast to the object is 50 degrees.
We can create a right-angled triangle to represent the situation. The horizontal line from the top of the mast to the object is the base of the triangle, and the height of the mast is the vertical side.
Now, we can use the tangent function because we have the opposite (height of the mast) and the adjacent (distance from the base of the mast to the object) sides.
The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.
So, we can write:
tan(50 degrees) = h / 6
To find the height of the mast 'h', we can rearrange the equation:
h = 6 * tan(50 degrees)
Now, we can use a calculator to find the value of the tangent of 50 degrees and multiply it by 6.
Using a calculator:
tan(50 degrees) ≈ 1.1918
Therefore, the height of the mast 'h' is approximately:
h ≈ 6 * 1.1918
Calculating this:
h ≈ 7.151 m
So, the height of the mast is approximately 7.15 meters when rounded to 2 decimal places.