After you are comfortable writing sine, cosine, tangent ratios you will often use sohcahtoa to find the sides of a right triangle. That is exactly what we are going to learn .
How to use sine, cosine, tangent to calculate x from diagram 1.
Write a table listing the givens and what you want to find:
| Givens | Want to Find |
|---|---|
| $$67 ^{\circ} $$ | Opposite |
| adjacent |
Set up an equation based on the ratio you chose in the step 2.
$ tan(67) = \frac{opp}{adj} \\ tan(67) = \frac{ \red x}{14} $
Solve the equation for the unknown.
$ tan(67) = \frac{ \red x}{14} \\ 14\times tan(67) = \red x \\ x \approx 32.98 $
Use sine, cosine or tangent to find the value of side x in the triangle below.
Write a table listing the givens and what you want to find:
| Givens | Want to Find |
|---|---|
| $$53 ^{\circ} $$ | opposite |
| Hypotenuse |
Set up an equation based on the ratio you chose in the step 2.
$ sin(53) = \frac{opp}{hyp} \\ sin(53) = \frac{\red x}{15} $
Solve for the unknown.
$ 15 \cdot sin(53) = \red x \\ x \approx 11.98 $
Use sine, cosine or tangent to find k in the triangle below.
Write a table listing the givens and what you want to find:
| Givens | Want to Find |
|---|---|
| $$53 ^{\circ} $$ | Hypotenuse |
| adjacent |
Set up an equation based on the ratio you chose in the step 2.
$ cos(53) = \frac{adj}{hyp} \\ cos(53) = \frac{45}{\red x} $
Solve for the unkown
$ \red x=\frac{45}{cos(53)} \\ x \approx 74.8 $
Use sine, cosine or tangent to find $$\red x $$ in the triangle below.
Write a table listing the givens and what you want to find:
| Givens | Want to Find |
|---|---|
| $$63 ^{\circ} $$ | Hypotenuse |
| adjacent |
Set up an equation based on the ratio you chose in the step 1.
$ cos(63) = \frac{adj }{ hyp } \\ cos(63) = \frac{3 }{\red x } $
Solve for the unkown
$ \red x = \frac {3} {cos(63)} \\ x = 6.6 $
Use sine, cosine or tangent to find $$\red x $$ in the triangle below.
Write a table listing the givens and what you want to find:
| Givens | Want to Find |
|---|---|
| $$53 ^{\circ} $$ | opposite |
| adjacent |
Set up an equation based on the ratio you chose in the step 2.
$ tan(53) = \frac{opp}{ adj } \\ tan(53) = \frac{\red x }{22 } $
Solve for the unkown
$ \red x = 22 \cdot tan(53) \\ x = 29.2 $
What are two distinct ways that you can find x in the triangle on the left?
Use SOHCAHTOA and set up a ratio such as sin(16) = 14/x. (From here solve for X). By the way, you could also use cosine.
Method 2Set up the following equation using the Pythagorean theorem: x2 = 482 + 142. (From here solve for X).
Here's a page on finding the side lengths of right triangles.
