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Sav [38]
3 years ago
12

Using the side lengths, determine whether the triangle is acute, obtuse, or right.

Mathematics
1 answer:
Andreas93 [3]3 years ago
4 0

Answer:

Step-by-step explanation:

In an acute triangle, the size of all the angles are less than 90 degrees. In a right triangle, the size of one angle which is also the largest is 90 degrees. In an obtuse triangle, the size of the largest angle is greater than 90 degrees but lesser than 180 degrees. Looking at the given triangle,

1) it is not obtuse because are the angles are smaller than 90 degrees

2) it is not right angle because Pythagorean theorem does not hold. It means

61² + 11² ≠ 91²

3842 ≠ 8281

Since the size of all the angles are below 90 degrees, then it is an acute triangle.

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Based on the diagram shown, find θ to the nearest degree.
sattari [20]

Answer:

  θ = 38°

Step-by-step explanation:

The lower right triangle is congruent to the upper left triangle, so we have θ and 20° being the two acute angles in the triangle. The law of sines tells you ...

  sin(θ)/9 = sin(20°)/5

  sin(θ) = (9/5)sin(20°)

  θ = arcsin(9/5·sin(20°)) ≈ 38°

___

Another solution to the triangle is θ = 180° -38° = 142°. The diagram clearly shows θ as an acute angle, so we take this second solution to be extraneous.

8 0
3 years ago
Integers are ____ rational numbers<br><br> 1. always<br> 2. sometimes<br> 3. never
yaroslaw [1]

I dont think the answer is always. Because integers are always whole numbers. Hope that helps a little?

6 0
3 years ago
Read 2 more answers
what is the ratio for the volumes of two similar spheres given that the ratio of their radii is 4:7 A.)343:64 B.)49:16 C.)16:49
quester [9]

Answer:

Volume of the similar sphere be 64 :343 .

Option (D) is correct.

Step-by-step explanation:

Formula

Volume\ of\ a sphere = \frac{4}{3}\pi r^{3}

As given

The volumes of two similar spheres given that the ratio of their radii is 4:7 .

Let us assume that the x be the scalar multiple of the radi .

Radius of first sphere = 4x

Radius of second sphere = 7x

Putting the values in the formula

Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 4x\times 4x\times 4x

Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 64x^{3}

Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 7x\times 7x\times 7x

Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 343x^{3}

Thus

\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{\frac{4\pi\times 64x^{3}}{3}}{\frac{4\pi\times 343x^{3}}{3}}

\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{64}{343}

Therefore the ratio of the volume of the similar sphere be 64 :343 .

Option (D) is correct .

5 0
3 years ago
Read 2 more answers
Four times a number increased by 8 is 54? ​
lawyer [7]

Answer:

4x+8=54 this is the correct answer

8 0
2 years ago
6. What is the slope of a line perpendicular to the line whose equation is y = 2x -5?*
bonufazy [111]

Answer: -1/2

You get y = 2x - 5, so the slope is 2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is -1/2.

6 0
3 years ago
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