Question

A plane takes a field and rises at an angle of 11.5 with the horizontal. Find the height of the plane after it has traveled a distance of 1240 ft. (Round answer to nearest decimal

Answer 1

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:

`\sin \theta=\frac{\text{opposite side}}{hypotenuse}`

Substituting:

`\sin 11.5^o=(h)/(1240)`

Solving for h:

`h=1240\cdot\sin 11.5^o`

Calculating:

`\begin{gathered} h=1240\cdot0.199368 \\ h=247.22\text{ ft} \end{gathered}`

The height of the plane is 247.22 ft