Find the Side Length of A Right Triangle

Sohcahtoa and the Pythagorean Theorem

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Related Links: sine, cosine , tangent | Pythagoren Theorem
Right Triangle Calculator

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There are many ways to find the side length of a right triangle. We are going to focus on two specific cases.

Case I When we know two sides of the right triangle, in which case, we will use the pythagorean theorem.

Case II When we know 1 side and 1 angle of the right triangle, in which case, we will use good old sohcahtoa.

Calculate the length of the sides below. In each case, round your answer to the neares hundredth.

Find the length of side X in the triangle below

Step 1 1) Since we know 2 sides of this triangle, we will use the pythagorean theorem to solve for x. Rest of Steps 2)Substitue the two known sides into the pythagorean theorem's formula: A² + B² = C² 8² + 6² = x² 100 = x²

Find the length of side X in the right triangle below

Step 1 1) Since we know 1 side and 1 angle of this triangle, we will use sohcahtoa. Step 2 2) Set up an equation using a sohcahtoa ratio. Since we know the hypotenuse and want to the side opposite of the 53° angle, we are dealing with sine Now, just solve the Equation: Answer 3) x = 15sin(53) = 11.98

Find the length of side t in the triangle below

Step 1 1) Since we know 2 sides of this triangle, we will use the pythagorean theorem to solve for side t. Rest of Steps 2)Substitue the two known sides into the pythagorean theorem's formula: A² + B² = C²

Find the length of side X in the right triangle below

Step 1 1) Since we know 1 side and 1 angle of this triangle, we will use sohcahtoa.. Step 2 2) Set up an equation using the sine, cosine or tangent ratio Since we know the length of the hypotenuse and side opposite of the 53° angle, we are dealing with sine Now, just solve the Equation: Answer 3) x = 24sin(67) = 22.09

Calculate the length of side X in the right triangle below

Step 1 1) Since we know 2 sides and 1 angle of this triangle, we can use either the pythagorean theorm ( by making use of the two sides ) or use sohcahto (by making use of the angle and 1 of the given sides) Step 2 2) Chose which way you want to solve this problem. There are several different solutions. The only thing you cannot use is sine, since the sine ratio does not involve the adjacent side, x, which we are trying to find. Pythagorean Theorem A² + B² = C² Using Cosine Using Tangent The answers are slightly different (tangent s 35.34 vs 36 for the others) due to rounding issues. I rounded the angle's measure to 23° for the sake of simplicity of the diagram. A more accurate angle measure would have been 22.61986495°. If you use tha value instead of 23°, you will get answers that are more consistent..