3-4-5 triangle
A 3-4-5 triangle is a special type of right triangle with side lengths in the ratio of 3:4:5
A 3-4-5 triangle is a special type of right triangle with side lengths in the ratio of 3:4:5. In this triangle, one angle is a right angle (90 degrees), and the other two angles are acute angles. The side opposite the right angle is called the hypotenuse.
To better understand the concept, let’s look at the triangle’s side lengths and angles:
– Side Lengths:
The side lengths of a 3-4-5 triangle are as follows:
– The side length opposite the smallest angle is 3 units.
– The side length opposite the second smallest angle is 4 units.
– The side length opposite the right angle (the hypotenuse) is 5 units.
– Angles:
A 3-4-5 triangle has three angles.
– One angle is a right angle, measuring 90 degrees.
– The other two angles are acute angles and can be found using trigonometric functions.
To find the angles in a 3-4-5 triangle, we can use trigonometric ratios. For example, using the side lengths given, we can find the sine, cosine, and tangent of each angle.
Using the sine function:
sin(A) = opposite/hypotenuse
sin(A) = 3/5
A ≈ 36.87 degrees
sin(B) = opposite/hypotenuse
sin(B) = 4/5
B ≈ 53.13 degrees
Using the cosine function:
cos(A) = adjacent/hypotenuse
cos(A) = 4/5
A ≈ 53.13 degrees
cos(B) = adjacent/hypotenuse
cos(B) = 3/5
B ≈ 36.87 degrees
Using the tangent function:
tan(A) = opposite/adjacent
tan(A) = 3/4
A ≈ 36.87 degrees
tan(B) = opposite/adjacent
tan(B) = 4/3
B ≈ 53.13 degrees
So, in summary, a 3-4-5 triangle is a right triangle with one side length measuring 3 units, another side measuring 4 units, and the hypotenuse measuring 5 units. The acute angles are approximately 36.87 degrees and 53.13 degrees.
More Answers:
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Understanding the Side Length Ratios in a 30-60-90 Triangle: Explained with Formulas and Summary