The height of the gymnastic mats is [tex]\dfrac{5 \times \sqrt{3}}{3}[/tex] feet.
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
Base is the adjacent smaller side of the angle θ.
As we can see in the below image the gymnastic mats are making the base of the right-angled triangle, therefore,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
[tex]Tan (\angle ACB) = \dfrac{Height}{BC}[/tex]
[tex]Tan (30^o) = \dfrac{Height}{5\ feet}[/tex]
[tex]\dfrac{1}{\sqrt{3}} = \dfrac{Height}{5\ feet}\\\\\dfrac{1 \times 5}{\sqrt{3}} = Height\\\\Height = \dfrac{5}{\sqrt{3}}[/tex]
Multiplying √3 with both denominator and numerator,
[tex]Height = \dfrac{5 \times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}\\\\Height = \dfrac{5 \times \sqrt{3}}{3}[/tex]
Hence, the height of the gymnastic mats is [tex]\dfrac{5 \times \sqrt{3}}{3}[/tex] feet.
Learn more about Tangent:
https://brainly.com/question/14022348
Answer: B
startFraction 5 StartRoot 3 EndRoot Over 3 EndFraction ft.
Step-by-step explanation:
