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mario62 [17]
2 years ago
9

A triangle has sides with lengths 5, 12, and 13. Verify this is a Pythagorean triple. Approximate the acute angles in this trian

gle.​
Mathematics
2 answers:
Molodets [167]2 years ago
8 0

The given numbers (can be taken as) the length of the three sides of a

(right) triangle.

Correct response:

  • 13² = 5² + 12², therefore,  5, 12, and 13 are a Pythagorean triple
  • The acute angles are; θ₁ ≈ 67.38°, and θ₂ ≈ 22.62°

<h3>Method of analysis to verify a Pythagorean triple</h3>

A Pythagorean triple are three positive integers, <em>a</em>, <em>b</em>, and <em>c</em> that are

related as follows;

c² = a² + b²

Therefore;

c = \mathbf{\sqrt{a^2 + b^2}}

Where;

a = 5, b = 12, we have;

\mathbf{\sqrt{5^2 + 12^2} } = 13 = c

Therefore;

  • <u>The three numbers form a</u><u> </u><u>Pythagorean triple</u>, the hypotenuse side (longest side = c = 13)

The acute angles are found as follows;

From trigonometric ratio, we have;

An \ tangent \ of \ acute \ angle \ \theta_1, \ \tan(\theta_1) = \dfrac{12}{5} = \mathbf{ 2.4}

Which gives;

  • An acute angle of the right triangle, θ₁ = arctan(2.4) ≈ <u>67.38°</u>

The acute angles of a right triangle are complimentary.

Therefore;

  • The other acute angle is therefore, θ₂ ≈ 90° - 67.38° = <u>22.62°</u>

Learn more about the Pythagorean theorem here:

brainly.com/question/18929869

djyliett [7]2 years ago
7 0

A triangle with lengths 5, 12, and 13 is a Pythagorean triple

The approximate acute angles are 22.6° and 67.4°

Pythagorean triple

Pythagorean triple consist of positive number(a, b, c) such that it obeys the rule:

  • c² = a² + b²

A triangle whose sides form a Pythagorean triple is called a right angle triangle.

The longest side is the hypotenuse side.

Therefore,

  • 5² + 12²
  • 25 + 144 = 169
  • √169  = 13

Therefore,

5² + 12² = 13²

This means the triangle is a Pythagorean triple.

<h3>Acute angles</h3>

Acute angles are angles that are less than 90 degrees. This means the other two angles are acute angle.

Therefore, let's find them

  • tan ∅ = opposite / adjacent = tan ∅ = 5 / 12 = ∅ = 22.6198649155 = 22.6°
  • 180 - 22.6 - 90 = 67.4°

learn more on Pythagorean triple here: brainly.com/question/2293263?referrer=searchResults

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