Long Side Of A Triangle

At that place are many ways to find the side length of a correct triangle. Nosotros are going to focus on two specific cases.

Example II

Nosotros know one side and 1 angle of the right triangle, in which example, use sohcahtoa.

Video Tutorial
on Finding the Side Length of a Right Triangle

Do Bug

Calculate the length of the sides beneath. In each case, round your respond to the nearest hundredth.

Problem one

Find the length of side X in the triangle below.

Stride 2

Substitute the two known sides into the Pythagorean theorem's formula:

$$ a^two + b^2 = c^2 \\ 8^2 + 6^2 = x^2 \\ 100 = ten^2 \\ x = \sqrt{100} \\ x = \boxed{x} $$

Problem 2

Find the length of side X in the right triangle beneath.

Stride ane

Since we know 1 side and one angle of this triangle, we will use sohcahtoa.

Step two

Fix an equation using a sohcahtoa ratio. Since nosotros know the hypotenuse and want to find the side opposite of the 53° angle, we are dealing with sine

$$ sin(53) = \frac{ contrary}{hypotenuse} \\ sin(53) = \frac{ \scarlet x }{ 12 } $$

Now, just solve the Equation:

Step 3

$$ sin(53) = \frac{ \red x }{ 12 } \\ \scarlet ten = 12 \cdot sin (53) \\ \cerise x = \boxed{ eleven.98} $$

Problem three

Find the length of side X in the right triangle below.

Step ii

Substitute the two known sides into the Pythagorean theorem'south formula:

$$ a^ii + b^2 = c^2 \\ \red t^2 + 12^2 = thirteen^two \\ \red t^2 + 144 = 169 \\ \red t^two = 169 - 144 \\ \ruby t^2 = 25 \\ \red t = \boxed{v} $$

Problem four

Find the length of side Ten in the right triangle beneath.

Step one

Since we know 1 side and 1 angle of this triangle, we will use sohcahtoa.

Step 2

Fix an equation using the sine, cosine or tangent ratio Since we want to know the length of the hypotenuse, and we already know the side opposite of the 53° bending, we are dealing with sine.

$$ sin(67) = \frac{opp}{hyp} \\ sin(67) = \frac{24}{\red x} $$

Now, just solve the Equation:

Step three

$$ x = \frac{ 24}{ sin(67) } \\ x = 26.07 $$

Problem 5

Calculate the length of side Ten in the right triangle beneath.

Step one

Since nosotros know 2 sides and 1 angle of this triangle, nosotros tin use either the Pythagorean theorem (by making use of the two sides) or utilize sohcahtoa (past making use of the angle and i of the given sides).

Step 2

Chose which way you desire to solve this problem. In that location are several different solutions. The only affair you cannot use is sine, since the sine ratio does not involve the adjacent side, x, which we are trying to detect.

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 authentic angle measure would have been 22.61986495°. If yous use that value instead of 23°, you will get answers that are more than consistent.

Step three

$$ ten = \frac{ 24}{ sin(67) } \approx 26.07 $$