Heights and Distances — Flashcards
ICSE · Class 10 · Mathematics
27 flashcards for Heights and Distances (ICSE Class 10 Mathematics) to test yourself on key terms and facts. Sample: "A building is seen from a point"
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A building is seen from a point on the ground. Which trigonometric idea helps find its height without measuring it directly?
Answer
Step 1: Identify the situation as a right-triangle problem. Step 2: Use trigonometric ratios. Step 3: Relate the known distance on the ground and the angle of elevation to the unknown height. Answer: …
When a point P is above the horizontal line OX, what is the angle ∠POX called?
Answer
Step 1: P is above the horizontal line OX. Step 2: The angle formed at O with the horizontal line is ∠POX. Answer: ∠POX is called the angle of elevation of P as seen from O.
When a point Q is below the horizontal line OX, what is the angle ∠QOX called?
Answer
Step 1: Q is below the horizontal line OX. Step 2: The angle formed at O with the horizontal line is ∠QOX. Answer: ∠QOX is called the angle of depression of Q as seen from O.
Why must the object and the observation point lie in the same vertical plane for angle of elevation or depression problems?
Answer
Step 1: The horizontal line OX is drawn in the same vertical plane as the object and observer. Step 2: This makes the line of sight and the horizontal reference line lie in one plane. Answer: The conc…
State the working rule for solving a right-triangle problem in applications of trigonometry.
Answer
Step 1: Make all the possible right angles. Step 2: Mark all given quantities or angles. Step 3: If more than one triangle is involved, assume the common side, often x. Step 4: Write trigonometric rat…
A problem has only one right triangle. Should the common side x be assumed in the working rule?
Answer
Step 1: The common side x is used when the figure has more than one triangle. Step 2: In a single triangle, there is no need for a common side. Answer: No. The common side x is assumed only for proble…
Solve: An observer sees the top of a tower at an angle of elevation. What should be the first step in drawing the figure?
Answer
Step 1: Draw the horizontal line through the observer. Step 2: Mark the tower as above the horizontal line. Step 3: Draw the line of sight from the observer to the top of the tower. Answer: The first …
Solve: An observer looks at a ship below the level of the eye line from a lighthouse. Which angle is formed?
Answer
Step 1: The ship is below the horizontal line from the observer. Step 2: The angle is formed at the observer between the line of sight and the horizontal line. Answer: The angle of depression is forme…
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