The Trigonometric Ratios
Some special relationships are defined between angles and side lengths in right triangles. These relationships are called Trigonometric Ratios.
Recall a right triangle is such that it has one angle of 90°.
Now let's take a look at the figure. The cell phone tower, the ground, and the line that joins the top of the tower and the ground form a right triangle.
It's required to find the angle of elevation marked with a question mark but we'll call it θ.
In front of θ, there is a side that measures 70 ft. Adjacent to θ, there is a side length of 45 ft. The tangent ratio relates one angle with opposite and adjacent sides as follows:
[tex]\tan \theta=\frac{\text{opposite side}}{adjacent\text{ side}}[/tex]Substituting values:
[tex]\text{tan}\theta=\frac{70}{45}=1.556[/tex]We know the value of the tangent of θ, now we find the value of the angle itself. It's required to use the inverse tangent function in any scientific calculator, Excel, or another similar tool. Thus
θ = arctan(1.556)
Calculating and rounding to hundredth as required:
θ = 57.26°
