Question

Triangle X Y Z is shown. Angle X Z Y is 63 degrees. The length of X Z is 2.7 and the length of X Y is 2.8. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction Which is the approximate measure of angle Y? Use the law of sines to find the answer. 52° 59° 64° 67°

Answer 1

Answer:

59°

Step-by-step explanation:

For the triangle XYZ the sine theorem states that

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

Since

$m\angle Z=63^{\circ}\\ \\XY=2.8\\ \\XZ=2.7,$

you have

$\dfrac{2.7}{\sin Y}=\dfrac{2.8}{\sin 63^{\circ}}\\ \\2.8\sin Y=2.7\sin 63^{\circ}\\ \\\sin Y=\dfrac{2.7\sin 63^{\circ}}{2.8}\\ \\\sin Y\approx 0.86\\ \\m\angle Y\approx 59^{\circ}$

Answer 2

The approximate measure of angle Y is 59° ⇒ 2nd answer

Step-by-step explanation:

The formula of the sine law of a triangle is $\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$ , where

• a is the side opposite the angle A
• b is the side opposite to angle B
• c is the side opposite to angle C

In Δ XYZ

∵ The side YZ is opposite to ∠X

∵ The side XZ is opposite to ∠Y

∵ The side XY is opposite to ∠Z

- Write the sine formula

∴  $\frac{sin(X)}{YZ}=\frac{sin(Y)}{XZ}=\frac{sin(Z)}{XY}$

∵ m∠XZY 63°

∵ The length of XZ = 2.7 units

∵ The length of XY = 2.8

- Substitute them in the sine formula

∴   $\frac{sin(63)}{2.8}=\frac{sin(Y)}{2.7}$

- By using cross multiplication

∴ 2.8 × sin(Y) = 2.7 × sin(63)

- Divide both sides by 2.8

∴ sin(Y) = 0.85918486

- Use the inverse of sine ($sin^{-1}$) to find y

∴ m∠Y = $sin^{-1}(0.85918486)$

∴ m∠Y ≅ 59°

The approximate measure of angle Y is 59°