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2 years ago

Explain why the value of the sine ratio for an acute angle of a right triangle must always be a positive value less than 1.

2 answers:

7 0

The sine of an angle x is defined as the ratio of the opposing side to the hypotenuse, in a right triangle having x as one of its acute angles. If it was greater than 1, it would mean the opposing side was longer than the hypotenuse. Try to draw a right triangle with one of the sides longer than the diagonal. You'll notice it's impossible. So the sine cannot be greater than 1.

<span>Fitting the triangle into a circle of radius 1, such that the angle x is located at the origin and the hypotenuse is a radius of the circle, you can define "sine of x" for any angle. Since the triangle may end up flipped in any direction, including the negative x and y axis, it turns out that the sine of any number is between -1 and +1.</span>

____ [38]2 years ago

3 0

The sine ratio is the length of the side opposite a given acute angle divided by the length of the hypotenuse. Because the hypotenuse is the side opposite the largest angle, the 90° angle, it has to be the longest side. Thus, the ratio will have a denominator that is larger than the numerator, and the ratio will be less than 1.

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Use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle. Show all work for full credit.

diamong [38]

Answer: The given triangle LMN is an obtuse-angled triangle.

Step-by-step explanation: We are given to use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle.

From the figure, we note that

in ΔLMN, LM = 5 units, MN = 13 units and LN = 14 units.

We know that a triangle with sides a units, b units and c units (a > b, c) is said to be

(i) Right-angled triangle if $b^2+c^2=a^2,$

(ii) Acute-angled triangle if $b^2+c^2>a^2,$

(iii) Obtuse-angled triangle if $b^2+c^2$

For the given triangle LMN, we have

a = 14, b = 13 and c = 5.

So,

$b^2+c^2=13^2+5^2=169+25=194,\\\\a^2=14^2=196.$

Therefore, $b^2+c^2$

Thus, the given triangle LMN is an obtuse-angled triangle.

5 0

2 years ago

In a school building, there are 8 exterior doors and 12 stairways to enter the second floor. Find a total number of ways to reac

Kazeer [188]

To reach the second floor you would look at all ways to enter to building(8) and multiply it by the number of ways to reach the second floor (12).

8 x 12 = 96 possibilities

Think of it in groups.

1st door and 12 possible sets of steps
2nd door and 12 possible sets of steps
3rd door and 12 possible sets of steps
4th door and 12 possible sets of steps
5th door and ..., etc.....

7 0

2 years ago

The perimeter of a triangle is 76cm side of the triangle is twice as long as side b .side c is 1 cm longer than a side a .find t

stepladder [879]

P= a+b+c = 76
side a = 2b = 30
side b = b = 15
side c = 2b + 1 = 31

7 0

2 years ago

How far should Galileo walk up the inclined plane?

sergejj [24]

Answer:

Step-by-step explanation:

150/x=sin 15

x=150/sin 15 ≈579.56 m

4 0

2 years ago

A formula calls for 0.6 mL of a coloring solution. Using a 10-mL graduate calibrated from 2 to 10 mL in 1-mL units, how could yo

MrMuchimi

Answer:

let us add 2.4 mL of water in 0.6 ml of coloring solution

total volume of solution = 2.4 + 0.6 = 3 mL

therefore,

0.6 mL of coloring solution now includes = 2.4ml of water

1 mL of coloring solution includes = 4mL of water

Hence

measure 3 mL of coloring solution with water that is formed

therefore, this 3 mL will contain 0.6 mL of coloring solution

Step-by-step explanation:

Given:

formula calls for 0.6 mL of a coloring solution

10-mL graduate calibrated from 2 to 10 mL in 1-mL units

Now,

We want to use an aliquot technique to measure 0.6 ml of coloring solution.

Because the calibrated graduate is used to measure 2ml to 10ml with 1ml as unit measure

let us add 2.4 mL of water in 0.6 ml of coloring solution

total volume of solution = 2.4 + 0.6 = 3 mL

therefore,

0.6 mL of coloring solution now includes = 2.4ml of water

1 mL of coloring solution includes = 4mL of water

Hence

measure 3 mL of coloring solution with water that is formed

therefore, this 3 mL will contain 0.6 mL of coloring solution

3 0

2 years ago