Angle from any type of Two Sides

We can find an unknown angle in a right-angled triangle, as lengthy as we know the lengths the two the its sides.

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The ladder leans against a wall surface as shown.

What is the angle in between the ladder and the wall?

The answer is to usage Sine, Cosine or Tangent!

But which one come use? We have a special expression "SOHCAHTOA" to assist us, and we use it like this:


Adjacent is surrounding to the angle, Opposite is the opposite the angle, and the longest side is the Hypotenuse.

Example: in ours ladder example we understand the length of:

the side Opposite the angle "x", which is 2.5 the longest side, called the Hypotenuse, i beg your pardon is 5

Step 2: currently use the an initial letters of those two sides (Opposite and also Hypotenuse) and the phrase "SOHCAHTOA" to discover which one of Sine, Cosine or Tangent come use:

In our instance that is Opposite and Hypotenuse, and that offers us “SOHcahtoa”, i m sorry tells united state we have to use Sine.

Step 4: now solve the equation!

sin(x) = 0.5

Next (trust me for the moment) we have the right to re-arrange that right into this:

x = sin-1(0.5)

And then obtain our calculator, vital in 0.5 and also use the sin-1 switch to get the answer:

x = 30°

But what is the meaning of sin-1 … ?

Well, the Sine function "sin" takes an angle and also gives united state the ratio "opposite/hypotenuse",


But sin-1 (called "inverse sine") go the other way ...... It takes the ratio "opposite/hypotenuse" and also gives united state an angle.

On the calculator press among the following (dependingon your brand of calculator):either "2ndF sin" or "shift sin".

On her calculator, shot using sin and also sin-1 to view what results you get!

Also shot cos and also cos-1. And tan and tan-1.Go on, have actually a try now.

Step by Step

These space the four steps we must follow:

step 1 discover which two sides we recognize – the end of Opposite, nearby and Hypotenuse.Step 2 usage SOHCAHTOA to decide which among Sine, Cosine or Tangent to use in this question. Step 3 for Sine calculation Opposite/Hypotenuse, because that Cosine calculation Adjacent/Hypotenuse or because that Tangent calculation Opposite/Adjacent.Step 4 uncover the angle from her calculator, using one of sin-1, cos-1 or tan-1


Let’s look at a pair more examples:



Find the angle of key of the airplane from point A on the ground.

action 1 The two sides we recognize are Opposite (300) and also Adjacent (400).Step 2 SOHCAHTOA tells united state we need to use Tangent. Step 3 calculate Opposite/Adjacent = 300/400 = 0.75 Step 4 discover the edge from her calculator utilizing tan-1

Tan x° = opposite/adjacent = 300/400 = 0.75

tan-1 of 0.75 = 36.9° (correct come 1 decimal place)

Unless you’re said otherwise, angles space usually rounded to one location of decimals.

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Find the size of angle a°

step 1 The 2 sides we recognize are Adjacent (6,750) and also Hypotenuse (8,100).Step 2 SOHCAHTOA tells us we have to use Cosine. Step 3 Calculate nearby / Hypotenuse = 6,750/8,100 = 0.8333 Step 4 discover the edge from her calculator using cos-1 that 0.8333:

cos a° = 6,750/8,100 = 0.8333

cos-1 the 0.8333 = 33.6° (to 1 decimal place)
250, 1500, 1501, 1502, 251, 1503, 2349, 2350, 2351, 3934
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