Triangle V U W is shown. The length of side W V is 6 centimeters, the length of side W U is 3 StartRoot 3 EndRoot centimeters, and the length of side U V is 3 centimeters. What are the angle measures of triangle VUW? m∠V = 30°, m∠U = 60°, m∠W = 90° m∠V = 90°, m∠U = 60°, m∠W = 30° m∠V = 30°, m∠U = 90°, m∠W = 60° m∠V = 60°, m∠U = 90°, m∠W = 30°

In any triangle if the sum of the squares of the shortest two sides is equal to the square of the longest side, then the triangle is a right triangle and the angle opposite to the longest side is the right angle

In Δ VUW

∵ WV = 6 cm

∵ WU = 3[tex]\sqrt{3}[/tex] cm

∵ UV = 3 cm

- Use the rule above tho check if it is a right Δ or not

∴ The longest side is WV

∴ The shortest two sides are WU and UV

∵ (WV)² = (6)² = 36

∵ (WU)² + (UV)² = (3[tex]\sqrt{3}[/tex] )² + (3)² = 27 + 9 = 36

∴ (WV)² = (WU)² + (UV)²

- That means ∠U which opposite to WV is a right angle

∴ Δ VUW is a right triangle at ∠U

∴ m∠U = 90°

Let us use the trigonometry ratios to find m∠W and m∠V

→ sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]

∵ UV is the opposite side of ∠W

∵ WV is the hypotenuse

∵ sin(∠W) = [tex]\frac{UV}{WV}[/tex]

∵ sin(∠W) = [tex]\frac{3}{6}=\frac{1}{2}[/tex]

- Use [tex]sin^{-1}[/tex] to find ∠W

∴ ∠W = [tex]sin^{-1}(\frac{1}{2})[/tex]

∴ m∠W = 30°

∵ WU is the opposite side of ∠V

∵ WV is the hypotenuse

∵ sin(∠V) = [tex]\frac{WU}{WV}[/tex]

∵ sin(∠V) = [tex]\frac{3\sqrt{3}}{6}=\frac{\sqrt{3}}{2}[/tex]

- Use [tex]sin^{-1}[/tex] to find ∠V

∴ ∠V = [tex]sin^{-1}(\frac{\sqrt{3}}{2})[/tex]

∴ m∠V = 60°

The angle measures of Δ VUW are m∠V = 60°, m∠U = 90°, m∠W = 30°

ilovek9es91 ilovek9es91 · Answer 2 · 2021-02-18T05:41:05+01:00

Answer:

The angle measures of Δ VUW are m∠V = 60°, m∠U = 90°, m∠W = 30° ⇒ last answer

Step-by-step explanation:

In any triangle if the sum of the squares of the shortest two sides is equal to the square of the longest side, then the triangle is a right triangle and the angle opposite to the longest side is the right angle

In Δ VUW

∵ WV = 6 cm

∵ WU = 3 cm

∵ UV = 3 cm

- Use the rule above tho check if it is a right Δ or not

∴ The longest side is WV

∴ The shortest two sides are WU and UV

∵ (WV)² = (6)² = 36

∵ (WU)² + (UV)² = (3 )² + (3)² = 27 + 9 = 36

∴ (WV)² = (WU)² + (UV)²

- That means ∠U which opposite to WV is a right angle

∴ Δ VUW is a right triangle at ∠U

∴ m∠U = 90°

Let us use the trigonometry ratios to find m∠W and m∠V

→ sin Ф =

∵ UV is the opposite side of ∠W

∵ WV is the hypotenuse

∵ sin(∠W) =

- Use to find ∠W

∴ ∠W =

∴ m∠W = 30°

∵ WU is the opposite side of ∠V

∵ WV is the hypotenuse

∵ sin(∠V) =

- Use to find ∠V

∴ ∠V =

∴ m∠V = 60°

So,the angle measures of Δ VUW are m∠V = 60°, m∠U = 90°, m∠W = 30°