Trigonometric Ratios - SOH CAH TOA - Free Printable

Looking at the triangle:

- It’s a right triangle (we can see the square symbol in the bottom-right corner).
- The side opposite angle “a” is labeled “3”.
- The side adjacent to angle “a” is labeled “4”.
- The hypotenuse (the side opposite the right angle) is labeled “5”.

This is a classic 3-4-5 right triangle — one of the most common Pythagorean triples. That means:
3² + 4² = 9 + 16 = 25 = 5² → so it checks out.

Now, we’re being asked about angle “a”. Since we know all three sides, we can find angle “a” using trigonometry.

The most straightforward way is to use the tangent function, because tangent of an angle in a right triangle is:

> tan(angle) = opposite / adjacent

For angle “a”:
- Opposite side = 3
- Adjacent side = 4

So:
tan(a) = 3/4 = 0.75

Now, to find the angle whose tangent is 0.75, we use the inverse tangent (also called arctangent):

a = arctan(0.75)

Using a calculator:
arctan(0.75) ≈ 36.87 degrees

We can also check with sine or cosine:

sin(a) = opposite/hypotenuse = 3/5 = 0.6 → arcsin(0.6) ≈ 36.87°
cos(a) = adjacent/hypotenuse = 4/5 = 0.8 → arccos(0.8) ≈ 36.87°

All methods give the same result.

So angle “a” is approximately 36.87 degrees.

Final Answer:
36.87°