Question

From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground? Five-halves ft StartFraction 5 StartRoot 3 EndRoot Over 3 EndFraction ft 5 StartRoot 3 EndRoot 10.

Answer 1

The height of the gymnastic mats is $\dfrac{5 \times \sqrt{3}}{3}$ feet.

Tangent (Tan θ)

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

$\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}$

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.

Given to us

• A right triangle with other angles measuring 60° and 30°.

• The gymnastics mat extends 5 feet across the floor.

Solution

As we can see in the below image the gymnastic mats are making the base of the right-angled triangle, therefore,

$\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}$

$Tan (\angle ACB) = \dfrac{Height}{BC}$

 $Tan (30^o) = \dfrac{Height}{5\ feet}$

$\dfrac{1}{\sqrt{3}} = \dfrac{Height}{5\ feet}\\\\\dfrac{1 \times 5}{\sqrt{3}} = Height\\\\Height = \dfrac{5}{\sqrt{3}}$

Multiplying √3 with both denominator and numerator,

$Height = \dfrac{5 \times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}\\\\Height = \dfrac{5 \times \sqrt{3}}{3}$

Hence, the height of the gymnastic mats is $\dfrac{5 \times \sqrt{3}}{3}$ feet.

Learn more about Tangent:

brainly.com/question/14022348

Answer 2

Answer: B

startFraction 5 StartRoot 3 EndRoot Over 3 EndFraction ft.

Step-by-step explanation: