Right triangle adjacent 4, opposite 4, find the angle Step by Step

Step by step

The question

Question: find the angle θ of a right triangle with adjacent side 4 and opposite side 4.

1 Name the sides

We look from the angle θ.

Every side gets a name from there.

The hypotenuse H is the longest side.

It is across from the right angle.

The opposite side O is across from our angle.

The adjacent side A is next to our angle.

It is not the hypotenuse.

2 Choose the ratio

SOH CAH TOA helps us remember.

Sin is O over H.

Cos is A over H.

Tan is O over A.

SOH CAH TOA

We have the adjacent and the opposite: A and O.

TOA has them.

So we use tan.

tan θ = OA

Careful!

From the other angle, the opposite and adjacent sides would swap.

Always name them from the angle we use.

Careful: O and A change with the angle

3 Write the equation

Now put the numbers in: O = 4 and A = 4.

tan θ = 44

4 divided by 4 is 1.

tan θ = 1

4 Turn it into the angle

The tan⁻¹ button on the calculator turns a ratio back into the angle.

tan⁻¹ : ratio → angle

So θ = tan⁻¹(1).

θ = tan⁻¹(1)

The calculator gives exactly 45.

So θ = 45°.

θ = 45°

5 Check

Let's check: tan of 45° on the calculator.

tan 45° = 1

That is 1 again.

So θ is right!

Let's look back.

First: name the sides.

Then: choose the ratio.

Then: write the equation.

Then: turn it into the angle.

Last: check.

Answer