Looking for the measurements of the interior angles of a triangle? Then check out this tutorial! You'll see how to use a given ratio of the interior angles and the Triangle Sum theorem to find those missing measurements. Take a look! Show We can find an unknown angle in a right-angled triangle, as long as we know the lengths of two of its sides. ExampleThe ladder leans against a wall as shown. What is the angle between the ladder and the wall?
The answer is to use Sine, Cosine or Tangent! But which one to use? We have a special phrase "SOHCAHTOA" to help us, and we use it like this: Step 1: find the names of the two sides we know
Example: in our ladder example we know the length of:
Step 2: now use the first letters of those two sides (Opposite and Hypotenuse) and the phrase "SOHCAHTOA" to find which one of Sine, Cosine or Tangent to use: SOH... Sine: sin(θ) = Opposite / Hypotenuse ...CAH... Cosine: cos(θ) = Adjacent / Hypotenuse ...TOA Tangent: tan(θ) = Opposite / Adjacent In our example that is Opposite and Hypotenuse, and that gives us “SOHcahtoa”, which tells us we need to use Sine. Step 3: Put our values into the Sine equation: Sin (x) = Opposite / Hypotenuse = 2.5 / 5 = 0.5 Step 4: Now solve that equation! sin(x) = 0.5 Next (trust me for the moment) we can re-arrange that into this: x = sin-1(0.5) And then get our calculator, key in 0.5 and use the sin-1 button to get the answer: x = 30° And we have our answer!But what is the meaning of sin-1 … ?Well, the Sine function "sin" takes an angle and gives us the ratio "opposite/hypotenuse", But sin-1 (called "inverse sine") goes the other way ... Example:
On the calculator press one of the following (depending on your brand of calculator): either '2ndF sin' or 'shift sin'. On your calculator, try using sin and sin-1 to see what results you get! Also try cos and cos-1. And tan and tan-1. Step By StepThese are the four steps we need to follow:
ExamplesLet’s look at a couple more examples: ExampleFind the angle of elevation of the plane from point A on the ground.
Tan x° = opposite/adjacent = 300/400 = 0.75 tan-1 of 0.75 = 36.9° (correct to 1 decimal place) Unless you’re told otherwise, angles are usually rounded to one place of decimals. ExampleFind the size of angle a°
cos a° = 6,750/8,100 = 0.8333 cos-1 of 0.8333 = 33.6° (to 1 decimal place)
250, 1500, 1501, 1502, 251, 1503, 2349, 2350, 2351, 3934 Random Trigonometry The Law of Sines The Law of Cosines Solving Triangles Trigonometry Index Algebra Index If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors. Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org. Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Please follow these steps to file a notice: You must include the following: A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf. |