Mathematics, 06.12.2019 17:31, pandapractice6834

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?

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answered: JohnBradley8657

The mat is 4.33 ft high off the ground.

Step-by-step explanation:

Since we have given that

Angle of elevation with the first triangle = 30°

Angle of elevation with the second triangle = 60°

Length at which gymnastics mat extends across the floor = 5 feet

so, As shown in the figure:

We need to find the height of the mat off the ground.

If CD = 5 ft,

Let, AB = y, DC = x.

In Δ ABC,

$\tan 60^\circ=\frac{AB}{BC}\\\\\frac{\sqrt{3}}{2}=\frac{y}{x}\\\\x=\frac{y}{\sqrt{3}}$

Similarly, in Δ ACD,

$\tan 30^\circ=\frac{AB}{BD}\\\\\frac{1}{\sqrt{3}}=\frac{y}{x+5}\\\\\frac{1}{\sqrt{3}}=\frac{y}{\frac{y}{\sqrt{3}}+5}\\\\\frac{1}{\sqrt{3}}=\frac{y\sqrt{3}}{y+5\sqrt{3}}\\\\3y=y+5\sqrt{3}\\\\2y=5\sqrt{3}\\\\y=\frac{5\sqrt{3}}{2}\\\\y=4.33\ ft$

Hence, the mat is 4.33 ft high off the ground.

From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°.

answered: gthif5424

Answer with explanation:

Description of gymnastic mat

Two interior angles of mat which is in the shape of right triangle are 60° and 30°.

Let the base and height of mat are x feet and y feet and Hypotenuse be z feet.

$sin 30=\frac{y}{z}\\\\ \frac{1}{2}=\frac{y}{z}\\\\z=2y$

$Tan30=\frac{y}{x}\\\\x=\sqrt{3}y$

Now, when mat extends 5 feet across the floor,angle of inclination will decrease that is will be less than 30° but the triangle will be a right triangle.

Length of base =(√3 y +5) Feet

Length of Hypotenuse = H feet> z>2 y

The height of gymnastic mat before and after extension will be same.

→→There is another possibility also.

If the total extension of the mat is 5 feet,then

$Base=\sqrt{3}y=5\\\\y=\frac{5}{\sqrt{3}}=\frac{5}{1.732}=2.886$

Length of base of mat =5 feet

Height of mat =2.89 feet(Approx)

answered: Guest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

answered: Guest

Set square i think so

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From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°....