Question

∆XYZ is a non-right triangle.if XY measures 20 cm,XZ measure 15 cm and angle Zmeasure 35°then wahat is the measure of angle Y

Answer 1

Answer:

The measure of angle Y is approximately 25°.

Step-by-step explanation:

∆XYZ is a non-right triangle. If XY measures 20 cm, XZ measures 15 cm, and angle Z measure 35°. Then, what is the measure of angle Y?

Given: non-right triangle XYZ, XY = 20 cm, XZ = 15 cm, angle Z = 35°

Asked: The measure of angle Y.

Solutions:

Use the Law of Sines because it s not a right triangle.

Applying the Law of Sines,

XZ/sin Y = XY/sin Z     The Law of Sines states that dividing the side by the sine of its opposite angle is equal to the other side divided by the sine of its opposite angle.

XZ/sin Y = XY/sin Z  Substitute the values of XZ, XY, and angle Z.

15/sin Y = 20/sin 35°   Apply cross multiplication.

20 (sin Y) = 15 (sin 35°)

20 sin Y = 15 (0.5736)  Use the table of sines to find the value of sin 35°.

(20 sin Y)/20 = [15 (0.5736)]/20  Apply Division Property of Equality.

sin Y = 8.604/20

sin Y  = 0.4302   Use the table of sines to find the measure of the angle.

Y = 25°

Angle Y is approximately 25°.

Answer 2

The answer is 25°

Given,

ΔXYZ is a non-right triangle.

XY = 20cm

XZ = 15cm

∠Z = 35°

To Find,

∠Y

Solution,

We will use the "Law of sines" to solve this problem.

By applying the Law of Sines,

$\frac{XY}{sin Z}$ = $\frac{XZ}{sin Y}$

Now, we will substitute the values we know.

$\frac{20}{sin 35}$ = $\frac{15}{sin Y}$

∴ sinY = $\frac{15 sin 35}{20}$

⇒ sin Y = $\frac{15(0.57)}{20}$

⇒ sin Y = $\frac{8.60}{20}$

⇒ sin Y = 0.43

⇒ Y = sin ⁻¹ (0.43)

⇒ Y ≅ 25°

Hence, ∠Y ≅ 25°