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°

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3 years ago

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What is the angle of pi over 2 radians?

Gwar [14]

The angle of pi over 2 radians is 90 degrees.

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3 years ago