Angles of Elevation and Depression Practice Questions
SPM (Malaysia) · SPM Mathematics · 150 free MCQs with instant results and detailed explanations.
150
Total
44
Easy
78
Medium
28
Hard
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Sample Questions from Angles of Elevation and Depression
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Q1
Easy
A kite is flying at an angle of depression of 30 degrees from a point 40 meters above the ground. How far is the kite horizontally from the base of the point?
A.
40√3 meters
B.
40 meters
C.
40√2 meters
D.
40√4 meters
Show Answer & Explanation
Correct Answer: A
The horizontal distance can be found using the formula: distance = height / tan(depression angle). Thus, distance = 40 / tan(30) = 40 * √3.
Q2
Easy
A ladder is leaning against a wall forming an angle of elevation of 45 degrees with the ground. If the base of the ladder is 10 meters away from the wall, how long is the ladder?
A.
10 meters
B.
5√2 meters
C.
20 meters
D.
15 meters
Show Answer & Explanation
Correct Answer: B
In a right triangle, if the angle is 45 degrees, the lengths of the opposite and adjacent sides are equal. Here, both sides are 10 meters, and using Pythagorean theorem, the ladder length (hypotenuse) is 10√2 meters.
Q3
Easy
A kite is flying at a height of 20 meters. If the angle of depression from the kite to a point on the ground is 45 degrees, how far is the point from the base of the kite vertically?
A.
20 meters
B.
10 meters
C.
30 meters
D.
45 meters
Show Answer & Explanation
Correct Answer: A
At an angle of depression of 45 degrees, the height equals the horizontal distance. Thus, the point is directly below the kite, 20 meters from the base.
Q4
Medium
A tower stands 50 meters tall. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?
A.
25√3 meters
B.
50 meters
C.
25 meters
D.
100 meters
Show Answer & Explanation
Correct Answer: A
To find the distance from the point to the base, use the tangent function. tan(30°) = height/distance, so distance = height/tan(30°) = 50/√3 = 25√3 meters.
Q5
Medium
A person is standing 40 meters away from the base of a building. If the angle of elevation from the person's eyes (1.5 meters above the ground) to the top of the building is 45 degrees, what is the height of the building?
A.
41.5 meters
B.
40 meters
C.
45 meters
D.
38.5 meters
Show Answer & Explanation
Correct Answer: A
Using the tangent function, tan(45°) = (height - 1.5)/40. Since tan(45°) = 1, we can set height - 1.5 = 40. Therefore, height = 41.5 meters.
Q6
Medium
From the top of a hill, the angle of depression to a car on the road is 20 degrees. If the hill is 100 meters high, how far is the car from the base of the hill?
A.
100 tan(20°) meters
B.
100 cot(20°) meters
C.
100 sin(20°) meters
D.
100 cos(20°) meters
Show Answer & Explanation
Correct Answer: B
Using the angle of depression, the distance from the base can be found using cotangent. The distance = height/cot(20°) = 100/cot(20°) = 100 tan(70°).
Q7
Medium
A kite is flying at a height of 30 meters. A person standing on the ground observes the kite at an angle of elevation of 60 degrees. How far is the person from the point directly beneath the kite?
A.
15√3 meters
B.
30 meters
C.
30√3 meters
D.
10√3 meters
Show Answer & Explanation
Correct Answer: A
Using the tangent function, tan(60°) = height/distance. So, distance = height/tan(60°) = 30/√3 = 15√3 meters.
Q8
Hard
A person is standing on a cliff that is 80 meters high. He spots a boat sailing in the ocean. If the angle of depression from the top of the cliff to the boat is 30 degrees, how far is the boat from the base of the cliff?
A.
80√3 meters
B.
40√3 meters
C.
80 meters
D.
40 meters
Show Answer & Explanation
Correct Answer: A
Using the angle of depression, the horizontal distance from the base of the cliff to the boat can be found using the formula: distance = height / tan(angle of depression). Here, distance = 80 / tan(30°) = 80 / (1/√3) = 80√3 meters.
Q9
Hard
A tower stands 50 meters tall. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. What is the horizontal distance from the point to the base of the tower?
A.
25√3 meters
B.
50√3 meters
C.
50 meters
D.
25 meters
Show Answer & Explanation
Correct Answer: A
Using the tangent function, tan(30°) = opposite/adjacent = 50/h. Therefore, h = 50/tan(30°) = 50/(√3/3) = 50*3/√3 = 25√3 meters.
Q10
Hard
From a point on the ground 80 meters away from the base of a building, the angle of elevation to the top of the building is 45 degrees. What is the height of the building?
A.
80√2 meters
B.
80 meters
C.
40 meters
D.
60 meters
Show Answer & Explanation
Correct Answer: B
At an angle of elevation of 45 degrees, tan(45°) = 1. So, the height (h) equals the distance from the base (80 meters). Thus, h = 80 meters.
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Angles of Elevation and Depression — SPM (Malaysia) SPM Mathematics Practice Questions Online
This page contains 150 practice MCQs for the chapter Angles of Elevation and Depression in SPM (Malaysia) SPM Mathematics. The questions are organized by difficulty — 44 easy, 78 medium, 28 hard — so you can choose the right level for your preparation.
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