The height of the ladder using trigonometric ratio is 9.8 feet.
What is trigonometry?
Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
The slanting height of the ladder = 10 foot
The ladder makes an angle = 78°
Let height of the ladder be 'h'.
The below diagram shows the ladder position.
The height of the ladder can be found by using trigonometric ratio,
[tex]sin \theta=\frac{perpendicular}{hypotenuse}[/tex]
⇒ [tex]sin78=\frac{h}{10}[/tex]
⇒ [tex]0.9781=\frac{h}{10}[/tex]
⇒ [tex]h=9.781[/tex] ≈ [tex]9.8[/tex]
Hence we can conclude that the height of the ladder using trigonometric ratio is 9.8 feet.
Learn more about trigonometry here
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