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

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) =

∵ sin(∠W) =

- Use to find ∠W

∴ ∠W =

∴ m∠W = 30°

∵ WU is the opposite side of ∠V

∵ WV is the hypotenuse

∵ sin(∠V) =

∵ 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°

Answer 2

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

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
`√(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
`√(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 =
`(opposite)/(hypotenuse)`

∵ UV is the opposite side of ∠W

∵ WV is the hypotenuse

∵ sin(∠W) =
`(UV)/(WV)`

∵ sin(∠W) =
`(3)/(6)=(1)/(2)`

- Use
`sin^(-1)` to find ∠W

∴ ∠W =
`sin^(-1)((1)/(2))`

∴ m∠W = 30°

∵ WU is the opposite side of ∠V

∵ WV is the hypotenuse

∵ sin(∠V) =
`(WU)/(WV)`

∵ sin(∠V) =
`(3√(3))/(6)=(√(3))/(2)`

- Use
`sin^(-1)` to find ∠V

∴ ∠V =
`sin^(-1)((√(3))/(2))`

∴ m∠V = 60°

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