Trigonometric Ratios
The trigonometric ratios are formulas that relate angles and sides in a right triangle.
A right triangle has an angle of 90°.
The situation described in the question can be represented by the first triangle, where the angle of elevation is 11.5° and the distance traveled is the hypotenuse of the triangle and its value is 1240 ft.
It's required to find the height h.
Considering the angle of elevation as a reference, the trigonometric ratio that can be used to find h is the sine.
The sine ratio is defined as:
[tex]\sin \theta=\frac{\text{opposite side}}{hypotenuse}[/tex]
Substituting:
[tex]\sin 11.5^o=\frac{h}{1240}[/tex]
Solving for h:
[tex]h=1240\cdot\sin 11.5^o[/tex]
Calculating:
[tex]\begin{gathered} h=1240\cdot0.199368 \\ h=247.22\text{ ft} \end{gathered}[/tex]
The height of the plane is 247.22 ft
