Solution Of Right Triangles
ICSE · Class 9 · Mathematics
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In a right triangle ABC with right angle at B, if angle A = 30° and BC = 10 cm, what is the length of AB?
If sin x° = 1/2, what is the value of x?
A ladder 13 meters long leans against a wall. If the foot of the ladder is 5 meters from the wall, what angle does the ladder make with the ground?
In triangle ABC, right-angled at B, if AB = 12 cm and BC = 16 cm, find AC.
Sample Questions
Which of the following are correct for a 45-45-90 triangle? (Select all correct answers)
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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.
If cos θ = √3/2, then θ equals:
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30°
From standard trigonometric values, cos 30° = √3/2. Step 1: Recall standard values: cos 30° = √3/2. Step 2: Therefore θ = 30°.
In a rhombus with side 8 cm and one angle 60°, what is the length of the shorter diagonal?
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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.
Which of the following statements about a 30-60-90 triangle are true? (Select all correct)
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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.
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