Question

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°

Answer 1

Answer:

D just took it

Step-by-step explanation:

Answer 2

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$\sqrt{3}$ 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$\sqrt{3}$ )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 = $\frac{opposite}{hypotenuse}$

∵ UV is the opposite side of ∠W

∵ WV is the hypotenuse

∵ sin(∠W) = $\frac{UV}{WV}$

∵ sin(∠W) = $\frac{3}{6}=\frac{1}{2}$

- Use $sin^{-1}$ to find ∠W

∴ ∠W = $sin^{-1}(\frac{1}{2})$

∴ m∠W = 30°

∵ WU is the opposite side of ∠V

∵ WV is the hypotenuse

∵ sin(∠V) = $\frac{WU}{WV}$

∵ sin(∠V) = $\frac{3\sqrt{3}}{6}=\frac{\sqrt{3}}{2}$

- Use $sin^{-1}$ to find ∠V

∴ ∠V = $sin^{-1}(\frac{\sqrt{3}}{2})$

∴ m∠V = 60°

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