A 25-foot extension ladder leaning against a building makes a 74 degree angle with the ground. How far up the building does the ladder touch?

Respuesta :

Given data:

* The actual length of the ladder is 25 foot.

* The angle made by the ladder with the ground is 74 degrees.

Solution:

The diagramatic representation of the given case is,

From the diagram,

Angle between the OA and OB is 90 degree.

Thus, the triangle AOB is the right angled triangle.

As the value of perpendicular of the triangle AOB in terms of the angle made by the ladder with the ground is,

[tex]\sin (\theta)=\frac{\text{Perpendicular (OA)}}{\text{Hypotenuse (BA)}}[/tex]

Thus, the value of OA is,

[tex]\begin{gathered} \sin (74^{\circ})=\frac{OA}{BA} \\ OA=BA\times\sin (74^{\circ}^{}) \end{gathered}[/tex]

Substituting the known values,

[tex]\begin{gathered} OA=25\times\sin (74^{\circ}) \\ OA=24.03\text{ foot} \end{gathered}[/tex]

Thus, the ladder touch the building at the distance of 24.03 foot above the ground (vertically).

Ver imagen TyrelD344902