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3 years ago

Could a triangle have side lengths of 1.2 ft 1.9ft and 3.1 ft

Mathematics

1 answer:

ss7ja [257]3 years ago

4 0

Answer:

No, a triangle could not have these side lengths.

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. Let's say side a = 1.2, b = 1.9, and c = 3.1, if we add a+b, then the sums are equal to side c. This would not satisfy the Triangle Inequality Theorem because one configuration of the equation results in the sum and third length being congruent, rather than greater.

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Urgent!! Will mark brainliest!!

anastassius [24]

Answer:

1) tanФ = 0.8392 ⇒ 2nd answer

2) cosФ = 20/29 ⇒ 3rd answer

3) cosФ = -√2/2 , cotФ = -1 ⇒ first answer

Step-by-step explanation:

* At first check the quadrant of the angle

∵ 180° < Ф < 270°

∴ Ф lies on the third quadrant

* Remember in the 3rd quadrant tanФ and cotФ only positive

∵ sinФ ≅ -0.7660

∵ tan²Ф = sec²Ф - 1

∵ secФ = 1/sinФ

∵ secФ = 1/-0.7660

∴ sec²Ф = (1/-0.7660)²

* Substitute this value in the equation

∴ tan²Ф = (1/-0.7660)² - 1 = 0.70428594 ⇒ take √ for both sides

∴ tanФ ≅ ± 0.8392

∵ Ф lies on the 3rd quadrant

∴ tanФ = 0.8392

* At first check the quadrant of the angle

∵ 0° < Ф < 90°

∴ Ф lies on the first quadrant

* Remember in the 1st quadrant all are positive

∵ sinФ = 21/29

∵ sin²Ф + cos²Ф = 1

∴ (21/29)² + cos²Ф = 1 ⇒ subtract (21/29)² from both sides

∴ cos²Ф = 1 - (21/29)² = 400/841 ⇒ take √ in both sides

∴ cosФ = ± 20/29

* Because Ф lies in the 1st quadrant

∴ cosФ = 20/29

* Remember that when the point is at the terminal side of angle Ф

∴ Its x-coordinate is cosФ

∴ Its y-coordinate is sinФ

* The point is (-√2/2 , √2/2)

∵ x-coordinate is negative ad y-coordinate is positive

∴ the point is on the 2nd quadrant

∴ 90° < Ф < 180°

∴ The values of sinФ and cscФ only positive

* From previous we know that:

∴ cosФ = -√2/2

∴ sinФ = √2/2

∵ cotФ = cosФ/sinФ

∴ cotФ = -√2/2 ÷ √2/2 = -√2/2 × 2/√2 = -√2/√2 = -1

* cosФ = -√2/2 , cotФ = -1

3 0

3 years ago

Find the inverse g(x)=x/5-6

STALIN [3.7K]

Interpreted: $g(x) = \frac{x}{5} - 6$
Let $y = g(x)$
$y = \frac{x}{5} - 6$
$x = \frac{y}{5} - 6$ (Interchange the x and y-values)

$\frac{y}{5} = x + 6$ (Solve for y)
$y = 5(x + 6)$

$\therefore g^{-1}(x) = 5(x + 6)$

4 0

3 years ago

Find the angle theta in radians. ( PLEASE SHOW STEPS )

yKpoI14uk [10]

Hello!

As you can see, we have a radius of 6. If we divide, this means that this is 2.5 radians. To convert radians to degrees we use the formula below.

$\frac{180}{ \pi }x$

First of all we divide 180 by pi.

180/ $\pi$ ≈57.3

Now we multiply by 2.5

57.3(2.5)=143.25°

Note that the angle we see is obtuse, or greater than 90°.

Therefore, ∠θ≈143.25°

Now we need to convert this back into radians. This can be represented by the equation below.

$\frac{ \pi }{180}x$

First we divide pi by 180 then multiply by our angle.

$\pi$ /180(143.25)≈2.5

Therefore, our angle theta is about 2.5 radians.

I hope this helps!

3 0

3 years ago

Read 2 more answers

Help please and thank you.

azamat

9.2 i think you have to round it up and it’s 9.5

4 0

3 years ago

A bike shop has 11 1111 red bikes, 3 33 blue bikes, 4 44 orange bikes, and 12 1212 silver bikes. For every 1 11 orange bike, the

zubka84 [21]

Answer:

C. Silver bikes

Step-by-step explanation:

Given that:

Number of red bikes at the bike shop = 11

Number of blue bikes at the bike shop = 3

Number of orange bikes at the bike shop = 4

Number of silver bikes at the bike shop = 12

Let us find the ratio of each bike with orange bikes to find the answer.

Orange bikes: Red bikes = 4 : 11

i.e. for every 4 orange bikes, there are 11 red bikes.

Orange bikes: Blue bikes = 4 : 3

i.e. for every 4 orange bikes, there are 3 blue bikes.

Orange bikes: Silver bikes = 4 : 12 = 1 : 3

i.e. for every 1 orange bike, there are 3 silver bikes.

Therefore, the answer is:

C Silver bikes

5 0

3 years ago