In ΔXYZ, y = 6.1 cm, z = 7.5 cm and ∠X=61°. Find the length of x, to the nearest 10th of a centimeter.

To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of lengths a, b, and c and an angle γ opposite side c, the following equation holds true:

c² = a² + b² - 2ab*cos(γ)

In this case, we know the lengths of sides y and z and the measure of angle X. We can let x = c, y = a, and z = b. Then we substitute these values into the Law of Cosines:

x² = y² + z² - 2yzcos(X) x² = (6.1 cm)² + (7.5 cm)² - 2(6.1 cm)*(7.5 cm)*cos(61°)

Now we just need to calculate the right side of the equation. Remember to convert the angle to radians if your calculator is set to that mode.

x² = 37.21 cm² + 56.25 cm² - 2*(6.1 cm)*(7.5 cm)cos(61°) x² = 93.46 cm² - 91.5 cm²cos(61°)

Calculate the cosine part:

x² = 93.46 cm² - 91.5 cm²*0.4848 x² = 93.46 cm² - 44.37 cm² x² = 49.09 cm²

Finally, we take the square root of both sides to solve for x:

x = sqrt(49.09 cm²) x = 7.0 cm

So, the length of side x is approximately 7.0 cm.

To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of lengths a, b, and c and an angle γ opposite side c, the following equation holds true:

c² = a² + b² - 2ab*cos(γ)

In this case, we know the lengths of sides y and z and the measure of angle X. We can let side x be c, side y be a, and side z be b. Then we can substitute these values into the Law of Cosines:

x² = y² + z² - 2yz*cos(X)

x² = (6.1 cm)² + (7.5 cm)² - 2*(6.1 cm)*(7.5 cm)*cos(61°)

Now we just need to calculate the right side of the equation and take the square root to find x.

x = sqrt((6.1 cm)² + (7.5 cm)² - 2*(6.1 cm)*(7.5 cm)*cos(61°))

After calculating, we find that x is approximately 5.3 cm to the nearest tenth of a centimeter.

To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of lengths a, b, and c and an angle γ opposite side c, the following equation holds true:

c² = a² + b² - 2ab*cos(γ)

In this case, we know the lengths of sides y and z and the measure of angle X. We can let side x be c, side y be a, and side z be b. Then we can substitute these values into the Law of Cosines:

x² = y² + z² - 2yz*cos(X)

x² = (6.1 cm)² + (7.5 cm)² - 2*(6.1 cm)*(7.5 cm)*cos(61°)

Now, we just need to calculate the right side of the equation and take the square root to find the length of x. Remember to round to the nearest tenth of a centimeter.