how to find the angle of a right triangle

There are many means to find the side length of a right triangle. We are going to focus on 2 specific cases.

Case II

Nosotros know 1 side and 1 angle of the correct triangle, in which case, use sohcahtoa.

Video Tutorial

on Finding the Side Length of a Right Triangle

Exercise Problems

Summate the length of the sides below. In each case, round your answer to the nearest hundredth.

Problem 1

Find the length of side 10 in the triangle below.

Step 2

Substitute the 2 known sides into the Pythagorean theorem's formula:

$$ a^2 + b^ii = c^ii \\ 8^2 + six^2 = x^2 \\ 100 = ten^two \\ 10 = \sqrt{100} \\ 10 = \boxed{10} $$

Problem two

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

Step 1

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

Stride 2

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

$$ sin(53) = \frac{ reverse}{hypotenuse} \\ sin(53) = \frac{ \cherry-red x }{ 12 } $$

Now, merely solve the Equation:

Stride iii

$$ sin(53) = \frac{ \ruby-red 10 }{ 12 } \\ \cherry x = 12 \cdot sin (53) \\ \cherry 10 = \boxed{ 11.98} $$

Problem 3

Find the length of side 10 in the correct triangle below.

Step two

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

$$ a^2 + b^ii = c^2 \\ \scarlet t^ii + 12^2 = 13^2 \\ \red t^2 + 144 = 169 \\ \red t^two = 169 - 144 \\ \red t^2 = 25 \\ \red t = \boxed{5} $$

Trouble 4

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

Stride 1

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

Footstep two

Set up 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° angle, nosotros are dealing with sine.

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

Now, just solve the Equation:

Step 3

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

Problem 5

Calculate the length of side X in the correct triangle beneath.

Pace 1

Since we know 2 sides and 1 angle of this triangle, we can use either the Pythagorean theorem (by making use of the ii sides) or use sohcahtoa (by making use of the angle and 1 of the given sides).

Footstep 2

Chose which way you want to solve this problem. At that place are several dissimilar solutions. The merely thing you cannot use is sine, since the sine ratio does not involve the side by side side, x, which we are trying to notice.

The answers are slightly unlike (tangent south 35.34 vs 36 for the others) due to rounding problems. I rounded the angle'due south measure to 23° for the sake of simplicity of the diagram. A more accurate angle measure would have been 22.61986495°. If you lot use that value instead of 23°, you will get answers that are more than consistent.

Pace 3

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

Source: https://www.mathwarehouse.com/geometry/triangles/right-triangles/find-the-side-length-of-a-right-triangle.php

Posted by: fluddrainglevers.blogspot.com

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