The right triangle has an angle of 53 degrees. The opposite side is 6.4cm long. What is the adjacent ?

tan(@) =opp/adj so tan53=6.4/adj

adj=6.4/tan53=6.4/1.3333=4.8

Well, since we're dealing with a right triangle, we can use trigonometry to figure this out! If the opposite side is 6.4cm and the angle is 53 degrees, we can use the tangent function. However, I must warn you, triangles can be pretty acute! Ha.. get it? Acute... acute triangle.. okay, I'll stop clowning around.

Anyway, using the tangent function, we can say that tan(53) = opposite/adjacent. Solving for the adjacent side, we get:

Adjacent = opposite / tan(53)
= 6.4cm / tan(53)

Now, let me just grab my trusty calculator... *tap tap tap* Okay, according to my calculations, the adjacent side is approximately 5.32cm. So, there you have it, the adjacent side measures about 5.32cm. Keep your triangles right and your humor light!

To find the length of the adjacent side of a right triangle, you can use the trigonometric function cosine.

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

In this case, we know the angle is 53 degrees and the length of the opposite side is 6.4 cm.

Step 1: Convert the angle from degrees to radians.
To use the trigonometric function, we need to convert the angle from degrees to radians. The formula to convert degrees to radians is:
radians = degrees * (π/180)

Given that the angle is 53 degrees:
radians = 53 * (π/180) ≈ 0.925 radians

Step 2: Use the cosine function to find the length of the adjacent side.
cosine of the angle = adjacent side / hypotenuse

Given that the opposite side is 6.4 cm, we can substitute these values into the formula:
cos(0.925) = adjacent side / hypotenuse

Step 3: Solve for the adjacent side.
Multiply both sides of the equation by the hypotenuse:
cos(0.925) * hypotenuse = adjacent side

Since we don't know the length of the hypotenuse, we can leave it as a variable. Let's call it "h":
cos(0.925) * h = adjacent side

Step 4: Substitute the opposite side into the equation.
We know that the opposite side is 6.4 cm:
cos(0.925) * h = 6.4 cm

Step 5: Solve for the adjacent side.
To isolate the adjacent side, divide both sides of the equation by cos(0.925):
adjacent side = 6.4 cm / cos(0.925)

Using a calculator, you can find the approximate value of the adjacent side by dividing 6.4 cm by the cosine of 0.925 radians.

To find the length of the adjacent side of a right triangle, you can use the trigonometric function called cosine (cos). The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In this case, we are given the length of the opposite side and the angle.

1. Since we have the angle, we can use the cosine function. Recall that the cosine of an angle is the ratio of the adjacent side to the hypotenuse.

cos(angle) = adjacent / hypotenuse

2. Rearranging the formula, we get:

adjacent = cos(angle) * hypotenuse

3. In this case, we are given the length of the opposite side, which is 6.4 cm. We need to find the hypotenuse to use in the formula.

4. To find the hypotenuse, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

hypotenuse^2 = opposite^2 + adjacent^2

Plugging in the given values:

hypotenuse^2 = 6.4^2 + adjacent^2

Simplifying:

hypotenuse^2 = 40.96 + adjacent^2

5. Since we want to find the length of the adjacent side, we can solve for it. Rearranging the formula:

adjacent^2 = hypotenuse^2 - 40.96

Taking the square root of both sides:

adjacent = sqrt(hypotenuse^2 - 40.96)

6. Now, substitute the given value of the length of the opposite side, which is 6.4 cm, into the equation:

adjacent = sqrt(hypotenuse^2 - 40.96)
= sqrt(6.4^2 - 40.96)
= sqrt(40.96 - 40.96)
= sqrt(0)
= 0

Therefore, the length of the adjacent side is 0 cm.