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Right Triangle – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Right TriangleRight Triangle – Definition, ExamplesTable of ContentsRight Angled Triangle Definition of Right Angled Triangle

A right angled triangle is a special type of triangle where one of the interior angles equals 90 degrees. In this triangle, the longest side is called the hypotenuse, which is opposite to the right angle. The other two sides that form the right angle are known as the base and the height. The right angle is always the largest angle in the triangle, and there cannot be any obtuse angles in a right triangle.

Right triangles can be classified into two main types. An isosceles right triangle has one 90-degree angle and two 45-degree angles. In this triangle, two sides have equal length. The second type is a scalene right triangle, which has one 90-degree angle while the other two angles have different measures. In a scalene right triangle, all three sides have different lengths.

Examples of Right Angled Triangle Example 1: Finding the Area Using the Pythagorean Theorem Problem:

The largest side of a triangle is 101010 cm. If the height of the triangle is 888 cm, determine the area using the Pythagorean theorem.

Right Angled Triangle

Step-by-step solution:

Step 1, Identify what we know. The hypotenuse (longest side) is 101010 cm and the height is 888 cm.

Step 2, Find the base using the Pythagorean theorem. According to this theorem, H2=b2+h2H^2 = b^2 + h^2H2=b2+h2 where HHH is the hypotenuse, bbb is the base, and hhh is the height.

Step 3, Substitute the known values into the formula: 102=b2+8210^2 = b^2 + 8^2102=b2+82

Step 4, Solve for bbb:

100=b2+64100 = b^2 + 64100=b2+64 b2=36b^2 = 36b2=36 b=36=6 cmb = \sqrt{36} = 6 \text{ cm}b=36​=6 cm

Step 5, Calculate the area using the formula: Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21​×base×height Area=12×6×8=24 square cm\text{Area} = \frac{1}{2} \times 6 \times 8 = 24 \text{ square cm}Area=21​×6×8=24 square cm

Example 2: Finding the Area with Known Side Ratios Problem:

The sides of the triangle are in the ratio 3:4:53:4:53:4:5. The perimeter is 840840840 m. Find its area.

Right Angled Triangle

Step-by-step solution:

Step 1, Let's call the sides 3x3x3x, 4x4x4x, and 5x5x5x where xxx is a value we need to find.

Step 2, Use the perimeter to find xxx:

Perimeter=3x+4x+5x=840 m\text{Perimeter} = 3x + 4x + 5x = 840 \text{ m}Perimeter=3x+4x+5x=840 m 12x=84012x = 84012x=840 x=84012=70x = \frac{840}{12} = 70x=12840​=70

Step 3, Calculate the actual side lengths:

3x=3×70=210 m3x = 3 \times 70 = 210 \text{ m}3x=3×70=210 m 4x=4×70=280 m4x = 4 \times 70 = 280 \text{ m}4x=4×70=280 m 5x=5×70=350 m5x = 5 \times 70 = 350 \text{ m}5x=5×70=350 m

Step 4, Identify the hypotenuse. Since 350350350 m is the longest side, it must be the hypotenuse. This means 210210210 m and 280280280 m are the base and height.

Step 5, Find the area using the formula:

Area=12×base×height=12×210×280=29,400 m2\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 210 \times 280 = 29,400 \text{ m}^2Area=21​×base×height=21​×210×280=29,400 m2 Example 3: Finding the Hypotenuse Length Problem:

What is the measure of the hypotenuse in a right triangle that has a height equal to 777 cm and the base equal to 555 cm?

Right Angled Triangle

Step-by-step solution:

Step 1, Identify what we know. The height is 777 cm and the base is 555 cm.

Step 2, Use the Pythagorean theorem to find the hypotenuse (HHH):

H2=b2+h2H^2 = b^2 + h^2H2=b2+h2

Step 3, Substitute the known values:

H2=52+72H^2 = 5^2 + 7^2H2=52+72

Step 4, Solve for HHH:

H2=25+49H^2 = 25 + 49H2=25+49 H2=74H^2 = 74H2=74 H=74 cmH = \sqrt{74} \text{ cm}H=74​ cm Comments(7)SSwimmerEvanNovember 6, 2025This glossary page on right triangles is great! I've used it to help my students understand the concept better. Thanks for the clear explanations!

YYogiAriaNovember 4, 2025I've used this right triangle definition with my students. It's clear and helps them grasp key concepts. Great for making learning fun!

PProfessorUmaNovember 4, 2025I've used this right triangle def for my students. It's clear & helpful, making tough concepts like Pythagorean theorem much easier to grasp!

NNatureLover95September 17, 2025I’ve been using this page to help my kids with their geometry homework, and the clear examples of right triangles really made a difference. The step-by-step solutions are super helpful!

NNatureLover85September 10, 2025I used this Right Triangle definition and examples to help my kid with their homework, and it worked wonders! The step-by-step explanations made tricky concepts like the Pythagorean theorem so much easier to understand. Great resource!

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