In Which of the Following Cases Can We Use the Law of Sines to Solve a Triangle?

How does SOHCAHTOA help the states find side lengths?

Video

Example of finding Side Length

How to use sine, cosine, tangent to calculate x from diagram ane.

Diagram 1

Step 1

Write a table listing the givens and what you lot want to notice:

Givens	Want to Detect
$$67 ^{\circ} $$	Reverse
side by side

Step 2

Based on your givens and unknowns, determine which sohcahtoa ratio to use.

In this case we want to utilise tangent because it's the ratio that involves the adjacent and opposite sides.

Footstep 3

Ready an equation based on the ratio you chose in the step two.

$ tan(67) = \frac{opp}{adj} \\ tan(67) = \frac{ \cerise 10}{xiv} $

Stride iv

Solve the equation for the unknown.

$ tan(67) = \frac{ \red x}{14} \\ 14\times tan(67) = \red ten \\ ten \approx 32.98 $

Practice Problems

Trouble i

Use sine, cosine or tangent to discover the value of side x in the triangle below.

Step 1

Write a table listing the givens and what you desire to observe:

Givens	Want to Find
$$53 ^{\circ} $$	opposite
Hypotenuse

Step 2

Based on your givens and unknowns, determine which sohcahtoa ratio to use.

The sine ratio is the ane that involves the opposite side and the hypotenuse .

Step 3

Set up an equation based on the ratio yous chose in the pace 2.

$ sin(53) = \frac{opp}{hyp} \\ sin(53) = \frac{\cherry x}{15} $

Step 4

Solve for the unknown.

$ fifteen \cdot sin(53) = \red 10 \\ 10 \approx 11.98 $

Problem 2

Use sine, cosine or tangent to detect m in the triangle below.

Footstep i

Write a table list the givens and what you desire to discover:

Givens	Desire to Notice
$$53 ^{\circ} $$	Hypotenuse
next

Pace 2

Based on your givens and unknowns, determine which sohcahtoa ratio to utilize.

The Cosine ratio is the one that involves the adjacent side and the hypotenuse .

Step iii

Fix up an equation based on the ratio you lot chose in the step ii.

$ cos(53) = \frac{adj}{hyp} \\ cos(53) = \frac{45}{\ruby x} $

Pace 3

Solve for the unkown

$ \ruby-red x=\frac{45}{cos(53)} \\ ten \approx 74.8 $

Trouble 3

Use sine, cosine or tangent to find $$\reddish 10 $$ in the triangle below.

Footstep 1

Write a table listing the givens and what you lot want to detect:

Givens	Want to Find
$$63 ^{\circ} $$	Hypotenuse
adjacent

Stride 2

Based on your givens and unknowns, make up one's mind which sohcahtoa ratio to employ.

The cosine ratio is the one that involves the next side and the hypotenuse .

Step 3

Set up an equation based on the ratio yous chose in the step 1.

$ cos(63) = \frac{adj }{ hyp } \\ cos(63) = \frac{3 }{\red x } $

Step three

Solve for the unkown

$ \red 10 = \frac {3} {cos(63)} \\ ten = 6.6 $

Problem 4

Use sine, cosine or tangent to detect $$\cherry x $$ in the triangle beneath.

Step i

Write a table list the givens and what you lot desire to find:

Givens	Want to Find
$$53 ^{\circ} $$	opposite
next

Step 2

Based on your givens and unknowns, determine which sohcahtoa ratio to utilise.

The tangent ratio is the one that involves the oppsite and the next sides.

Stride 3

Ready upward an equation based on the ratio you chose in the step 2.

$ tan(53) = \frac{opp}{ adj } \\ tan(53) = \frac{\ruddy x }{22 } $

Pace iii

Solve for the unkown

$ \blood-red x = 22 \cdot tan(53) \\ x = 29.2 $

Problem 5

What are two distinct ways that you can find x in the triangle on the left?

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Source: https://www.mathwarehouse.com/trigonometry/sine-cosine-tangent-practice3.php

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