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2 years ago

Find the length of the hypotenuse. The measure of the hypotenuse?

Mathematics

2 answers:

Eduardwww [97]2 years ago

8 0

Answer:

Since it's a right angled triangle

Hypotenuse = h

h² = 7²+24²

h= √49 + 576

h = √625

h= 25

Therefore hypotenuse is 25

Hope this helps.

kow [346]2 years ago

6 0

Answer & Step-by-step explanation:

First, we must know the Pythagorean Theorem.

a² + b² = c²

a = 24

b = 7

Now, let's plug in these numbers into the formula.

24² + 7² = c²

Simplify the exponents.

576 + 49 = c²

Add 576 and 49 together.

625 = c²

Square root the terms on both sides of the equation.

√625 = √c²

Simplify the square roots.

25 = c

The length of the hypotenuse is 25 units.

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Given the following trigonometric ratio, enumerate the meaning ratio

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The trigonometric ratios are presented below:

$\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}$

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Step-by-step explanation:

From Trigonometry we know the following definitions for each trigonometric ratio:

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$\sin \theta = \frac{y}{h}$ (1)

Cosine

$\cos \theta = \frac{x}{h}$ (2)

Tangent

$\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}$ (3)

Cotangent

$\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y}$ (4)

Secant

$\sec \theta = \frac{1}{\cos \theta} = \frac{h}{x}$ (5)

Cosecant

$\csc \theta = \frac{1}{\sin \theta} = \frac{h}{y}$ (6)

Where:

$x$ - Adjacent leg.

$y$ - Opposite leg.

$h$ - Hypotenuse.

The length of the hypotenuse is determined by the Pythagorean Theorem:

$h = \sqrt{x^{2}+y^{2}}$

If $y = AC$ and $x = BC$ , then the trigonometric ratios are presented below:

$\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}$

$\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}$

$\cot \theta = \frac{BC}{AC}$

$\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}$

$\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}$

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2 years ago