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3 years ago

What is the maximum possible value of a sine ratio? In two or more complete sentences, explain your answer.

Mathematics

2 answers:

Natalka [10]3 years ago

8 0

Answer:

Step-by-step explanation:

The maximum possible value of a sine ratio is 1. This is because the formula to figuring out the sine is opposite leg/hypotenuse. Since the hypotenuse of a triangle is ALWAYS the longest side of the triangle, and it's the denominator of the formula, then the value of a sine ratio will never exceed 1.

Examples: (Bold = hypotenuse)

3/5 = 0.6

6/8 = 0.75

If there would be a leg longer than the hypotenuse (which is not possible), then the answers would be greater than 1:

5/3 = 1.666666667

8/6 = 1.333333333

Hope this helps!

VMariaS [17]3 years ago

6 0

The sine ratio is basically a fraction of the opposite side over the hypotenuse. Since the hypotenuse is always the longest side, this means the fraction cannot exceed 1. If it did,then that would lead to the opposite side being larger than the hypotenuse but again the hypotenuse is the longest side. The largest the sine ratio can get is 1.

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Leno4ka [110]

Answer:

a = $\sqrt{7}$

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.:

Suppose ABC is a right triangle with sides a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the values of the six trigonometric functions for angle B. when b=3 and c=4.

My answer:

We will Pythagoras theorem, which states that the sum of squares of two legs of a right triangle is equal to the square of the hypotenuse of right triangle. Because the question says that ABC is a right triangle.

$a^2+b^2=c^2$

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$a^2+3^2=4^2a^2+9=16a^2+9-9=16-9a^2=7$

so a = $\sqrt{7}$

We know that tangent relates opposite side of a right triangle with adjacent side.

$\text{tan}(B)=\frac{a}{b}\\\text{tan}(B)=\frac{\sqrt{7}}{3}$

Please have a look at the attached photos.

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