Usando coseno para calcular ángulos y lados (Cos = ah \frac{a}{h} )

You’re one step closer to a better grade.

Learn with less effort by getting unlimited access, progress tracking and more.

Learn More



  1. ¿Qué son el seno, coseno y tangente?



  1. Determina los ángulos y lados usando la razón de Coseno:
    1. Encuentra el ángulo AA y BB usando coseno:
      Use cosine ratio to calculate angle
    2. Encuentra el valor de "xx" usando coseno:
      Use cosine ratio, adjacent side and cosine theta to find hypotenuse

Become a Member to Get More!

  • Easily See Your Progress

    We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.

  • Make Use of Our Learning Aids

    Last Viewed
    Practice Accuracy
    Suggested Tasks

    Get quick access to the topic you're currently learning.

    See how well your practice sessions are going over time.

    Stay on track with our daily recommendations.

  • Earn Achievements as You Learn

    Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.

  • Create and Customize Your Avatar

    Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

Topic Basics
El coseno se define como la razón entre la medida del lado adyacente al ángulo en cuestión sobre la medida de la hipotenusa en un triángulo rectángulo.

Trigonometric ratios

cosine rule

The cosine rule tells us that when we have a right triangle, cosine=ahcosine = \frac{a}{h}. The "a" in this case stands for adjacent. The "h" stands for the hypotenuse, which can be found through the pythagorean theorem. In order to find cosine, all you'll need is the adjacent side and the hypotenuse.

sine rule

When you come across sine, you can find the answer for it in a right triangle by taking the opposite side over the hypotenuse in the form of sine=ohsine = \frac{o}{h}.

tangent rule

For the tangent rule, when you have a right triangle, you can use the opposite over the adjacent sides of the triangle to find your ratio. This means that tan=oatan = \frac{o}{a}.


When you hear SohCahToa, it's not immediately obvious what it means. But it's actually an easier way for you to remember how to use sine, cosine, tangent that we just learned. These three are the main functions that you'll deal with in trigonometry problems.

Soh Cah Toa stands for:

Sine, opposite, hypotenuse, Cosine, adjacent, hypotenuse, Tangent, opposite, adjacent
Soh Cah Toa table

It can help you find the length of a side of a right triangle as long as you have an angle θ\theta and some info on the other sides of the triangle.

Example problems

In this chapter, we're actually going to focus on the cosine rule. This means we'll only be working with the "CahCah" portion of SohCahToaSohCahToa. Try out the following trig problems alongside us to learn how to solve questions using the cosine rule.

Question 1

Determine each cosine ratio using calculator

a) cos\cos 50°

Simply put the number into your calculator and you should get 0.640.64.

b) cos\cos -50°

Simply put the number into your calculator and you should get 0.640.64.

cos\cos 50° and cos\cos -50° both = 0.640.64. Why?

Chart of all, sine, tangent, cosine
ASTC chart

This above ASTC chart helps you figure out which trig ratio is positive in which quadrant. cos\cos 50° lies in quadrant I, where all the trig ratios are positive. cos\cos -50° lies in quadrant 4, where cosine is positive. This is why we get 0.640.64 for both cos\cos 50° and cos\cos -50°.

Question 2

Determine the angle to the nearest degree


a) cosθ=0.24\cos \theta = 0.24

Use the inverse cosine in the calculator which has a little 1-1 beside coscos:

arccos(0.24)=76\arccos (0.24) = 76°

b) cosθ=0.45\cos \theta = -0.45

Use the inverse cosine in the calculator to find:

arccos(0.45)=117\arccos (-0.45) = 117°

Question 3

Determine the angles and sides using cosine


a) Find angle AA and BB:

Finding angle A and B with the information provided
Find angle A and B

cosθ=adjacenthypotenuse\cos \theta = \frac{adjacent}{hypotenuse}

Angle AA

cosA=817\cos A = \frac{8}{17}

To solve it in your calculator

arccos817=62\arccos \frac{8}{17} = 62°

Angle BB

cosB=1517\cos B = \frac{15}{17}

To solve it in your calculator

arccos1517=28\arccos \frac{15}{17} = 28°

b) Find the value of "xx" using cosine

Find the side of the triangle x using cosine
Find x using cosine/figcaption>

cosθ=adjacenthypotenuse\cos \theta = \frac{adjacent}{hypotenuse}

cos\cos 32° = 25(x)\frac{25}{(x)}

x=25cos32x = \frac{25}{\cos 32}

x=29x = 29

Still curious about the cosine rule? Try out this online law of cosines calculator!

Next up, you're going to learn more about the law of cosines, how to find exact trigonometric ratios, and touch on what the unit circle is in trigonometry.