Sharpen your quantitative aptitude skills with this quiz focused on height and distance problems, including practical scenarios involving angles of elevation and depression. Ideal for those preparing for aptitude tests, this quiz reinforces important geometry concepts used in competitive exams.
A person stands 20 meters away from a tree and observes the top of the tree at an angle of elevation of 45 degrees. What is the height of the tree?
Explanation: When the angle of elevation is 45 degrees and the distance from the object is 20 meters, the height of the tree will also be 20 meters, due to the property of the right triangle where the opposite and adjacent sides are equal at 45 degrees. The distractors 15 meters and 10 meters result from incorrect calculations with the tangent ratio, and 25 meters confuses the relationship further. Only 20 meters correctly fits the trigonometric relationship.
From the top of a 60-meter tall tower, the angle of depression to a car on the ground is 30 degrees. How far is the car from the base of the tower?
Explanation: Using the formula distance = height / tan(angle), the correct answer is 60 / tan(30°) which is approximately 104 meters. The option 87 meters comes from using sine incorrectly, 34.6 meters from using tangent in reverse, and 120 meters is almost double the correct value, likely a calculation mix-up. Only 104 meters matches the correct trigonometric approach.
The angle of elevation to the top of a pole from a point 40 meters away is 60 degrees. What is the approximate height of the pole?
Explanation: The height can be found by 40 × tan(60°), which equals about 69.3 meters. The 34.6 meters and 40 meters options misuse either sine or cosine, and 20 meters is an arbitrary figure, not linked to the tangent function for 60 degrees. Only 69.3 meters is consistent with the given values and trigonometric calculation.
If the shadow of a building is 24 meters long and the angle of elevation of the sun is 45 degrees, what is the height of the building?
Explanation: At an angle of 45 degrees, the height of the object equals the length of its shadow, so the height of the building is 24 meters. 12 meters is half and would result from an incorrect halving, 34 and 48 meters are higher values not justified by the given scenario. Only 24 meters fits the properties of a 45-degree right triangle.
A ladder 10 meters long rests against a wall making an angle of 30 degrees with the ground. What is the height at which the ladder touches the wall?
Explanation: The height can be calculated with the sine function: height = 10 × sin(30°) = 5 meters. 10 meters assumes the ladder is vertical, 8.7 meters would result from using cosine instead, and 15 meters exceeds the actual ladder length, which isn't possible. Therefore, 5 meters is the correct answer based on trigonometric relationships.