Question

In triangle XYZ, given that x = 770 cm, z = 280 cm, and ∠ Z = 22°, find all possible values of angle X, to the nearest degree?

Answer 1

In triangle XYZ, given that x = 770 cm, z = 280 cm, and ∠ Z = 22°, the possible values of angle X are approximately 25.4°.

Step-by-step explanation:

In triangle XYZ, given that x = 770 cm, z = 280 cm, and ∠ Z = 22°, we can use the Law of Sines to find angle X. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant.

Applying this, we have:

sin X / x = sin Z / z

sin X / 770 = sin 22° / 280

Now, we can cross-multiply and solve for sin X:

sin X = (770 * sin 22°) / 280

Using a calculator, we find that sin X ≈ 0.422.

Next, we can use the inverse sine function to find the possible values of angle X:

X = sin⁻¹(0.422)

Using a calculator, we find that X ≈ 25.4°.

Therefore, the possible values of angle X in triangle XYZ are approximately 25.4°.

Answer 2

To find the possible values of angle X in triangle XYZ, subtract the given angle Z from 180° and subtract the sum from angle Y.

Step-by-step explanation:

To find the possible values of angle X in triangle XYZ, we can use the fact that the sum of the angles in a triangle is always 180°.

Since we know that angle Z is 22°, we can subtract this angle from 180° to find the sum of angles X and Y.

Therefore, angle X = 180° - angle Z - angle Y.