A rectangle is 14cm wide and 48 cm long. Find the measures of the acute angle between its diagonals.
please help
The diagonals cross in the center, so the acute angle is the vertex of an isosceles triangle with
height=24
base=14
so the acute angle x obeys
tan(x/2) = 7/24
To find the measures of the acute angle between the diagonals of a rectangle, we can use the formula:
θ = arctan(b/a)
where
θ is the angle between the diagonals,
b is the shorter side of the rectangle,
and a is the longer side of the rectangle.
In this case, the shorter side (b) of the rectangle is 14 cm and the longer side (a) is 48 cm.
Substituting the values into the formula:
θ = arctan(14/48)
Now we need to calculate the arctan(14/48). Let's use a calculator to find the value.
arctan(14/48) ≈ 16.84 degrees
Therefore, the acute angle between the diagonals of the rectangle is approximately 16.84 degrees.