Combination of SohCahToa questions

All You Need in One Place

Everything you need for better marks in primary, GCSE, and A-level classes.

Learn with Confidence

We’ve mastered the UK’s national curriculum so you can study with confidence.

Instant and Unlimited Help

24/7 access to the best tips, walkthroughs, and practice questions.

  1. Find the length of BC‾ \overline{ BC}

    Combination of SohCahToa questions
    1. Find the length of BD‾ \overline{ BD}

      Combination of SohCahToa questions
      Free to Join!
      StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
      • 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 Notes
      SOHCAHTOA is actually a memory aid to memorize how to calculate sine, cosine and tangent of an angle. SOH: sine = opposite over hypotenuse; CAH = adjacent over hypotenuse; and TOA = opposite over adjacent. Besides using them separately, the sine, cosine, and tangent ratios can be used together to solve trigonometry problems.

      What is SohCahToa?

      When you hear SohCahToa, it may sound like a different language entirely. But it's actually an easier way for you to remember how to use sine, cosine and tangent. These three are the main functions that you'll deal with in trigonometry problems.

      SohCahToa stands for:

      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.

      Is SohCahToa only for right triangles

      Yes, SohCahToa is only for right triangles. That's because only right triangles have a hypotenuse. Depending on which angle (whichever angle it is, it's called the angle θ\theta) you're using, you'd then figure out what the opposite or the adjacent is.

      The adjacent side is always next to the angle. It's the side next to the angle that is not the hypotenuse. The opposite side is simply the side that's opposite of the angle.

      Once you have several of the components given to you in a question, you'll be able to figure out unknowns that aren't given! You should also review how to find hypotenuse before we proceed. We'll try a question below to put Soh Cah Toa into use.

      how to use SohCahToa

      Question 1:

      Find the length of BC‾\overline{BC}


      △\triangleABD is a right angle triangle by itself. This means we can look for AB‾\overline{AB} using tan. Tan takes the opposite over the hypotenuse (Toa in SohCahToa).

      tan⁡22\tan 22° =AB‾80= \frac{\overline{AB}}{80}

      AB‾=32.3cm\overline{AB}= 32.3 cm

      Now that we've got AB‾\overline{AB}, we can look for AC‾\overline{AC} using tan. △\triangleACD is also a right angle triangle, so we can use SohCahToa. Again, we're making use of Toa in SohCahToa.

      tan⁡37\tan 37° =AC‾80= \frac{\overline{AC}}{80}

      AC‾=60.3cm\overline{AC}= 60.3 cm

      We know the lengths of AB‾\overline{AB} and AC‾\overline{AC}, which means we can subtract the length of AB‾\overline{AB} from AC‾\overline{AC} in order to just get the length of BC‾\overline{BC}.

      BC‾=\overline{BC} = AC‾−\overline{AC} - AB‾\overline{AB}

      BC‾=60.3−32.3\overline{BC} = 60.3-32.3

      = 28 cm

      A lot of the questions you'll be given require you to put to use several of the trig ratios. You'll always be working with right triangles, so make sure to keep a note of that when you start the question. For example, this question seemed to require you to use △\triangleBCD at first, but you know that can't be right because it is not a right triangle. Without that 90 degree right angle, you won't be able to use SohCahToa to help you find the unknowns.

      Always base your answers around the right triangles in the question and you'll be able to find the answer.

      Up for a challenge? Try out this online math test to see if you can answer these trigonometry questions quizzing you on Soh Cah Toa.

      A lesson to review that deals with sine, cosine, and tangent includes the ASTC rule. You can also look into these lessons that covers how to find unknowns using the law of sines and the law of cosines. Studying how to find exact values of trigonometric ratios and trig ratios of angles in radians will also advance you further in trig problems