Solution Of Right Triangles — Important Questions

sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1, The two legs are equal

In a 45-45-90 triangle: sin 45° = cos 45° = 1/√2, tan 45° = 1, and the two legs are equal. Step 1: Recall that 45-45-90 is an isosceles right triangle. Step 2: Both acute angles are 45°, so sin and cos values are equal. Step 3: tan 45° = 1 since opposite = adjacent.

30°

From standard trigonometric values, cos 30° = √3/2. Step 1: Recall standard values: cos 30° = √3/2. Step 2: Therefore θ = 30°.

8 cm

In a rhombus, diagonals bisect each other at right angles and bisect the vertex angles. If vertex angle is 60°, half-angle is 30°. Using sin 30° = (half shorter diagonal)/side: 1/2 = (half shorter diagonal)/8, so half shorter diagonal = 4 cm, making shorter diagonal = 8 cm. Step 1: Understand rhombus properties. Step 2: Use half-angle = 30°. Step 3: Apply sin 30° = 1/2.

The sides are in ratio 1 : √3 : 2, sin 60° = √3/2, cos 60° = 1/2, tan 30° = 1/√3

In a 30-60-90 triangle: sides are in ratio 1:√3:2, sin 60° = √3/2, cos 60° = 1/2, tan 30° = 1/√3. The hypotenuse is 2 times the shorter side, not √2 times. Step 1: Recall 30-60-90 triangle properties. Step 2: Verify each trigonometric ratio. Step 3: Check side ratios.