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3 years ago

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

Mathematics

2 answers:

kotykmax [81]3 years ago

5 0

Answer:

Step-by-step explanation:

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.

weqwewe [10]3 years ago

4 0

Answer: See below.

The sine ratio is the ratio of the opposite side over the hypotenuse in a right triangle. The hypotenuse is always the largest side of a triangle.

Therefore, the denominator will always be the largest. If the denominator is larger than the numerator, it will be a number less than one.

And it will be positive because it is an acute angle so the triangle when plotting in the unit circle would only be in the first quadrant. All values in the first quadrant are positive.

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3 years ago

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jek_recluse [69]

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3 years ago

Read 2 more answers

What is the radius of circle c

Oxana [17]

Answer:

radius = 13

Step-by-step explanation:

Look at the attached picture below. We can calculate radius with the help of the Pythagorean theorem. But first we have to find out the values of the two legs.

First let's find the shorter leg.

Equidistant Chords Theorem

Two chords are congruent if they are equidistant from the center.

Chords in the picture are congruent and that means that the distance from the center to each of them is the same!

Let's calculate the distance. But to get the distance we have to find x first.

Since the distances are the same:

$x + 3 = 2x + 1\\2 = x$

Therefore:

$\text{distance (short leg)} = 2x + 1 = 2\cdot2 + 1 = 5$

Let's focus on the longer leg. Since part of the radius is perpendicular to the chord, it actually bisects the chord! That means that the long leg is going to be a half of the length of the chord.

Therefore:

$\text{long leg} = \frac{\text{chord}}{2} = \frac{24}{2} = 12$