Angle from Any Two SidesWe can find an unknown angle in a right-angled triangle, as long as we know the lengths of two of its sides. Show 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:
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 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 |