Solve for the unknown variable(s) in each of the following.
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Question No. 3
Calculate the value of the unknown angles. Give reasons for your answers.
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Question No. 4
Find the unknown angle in each of the following.
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Question No. 5
Complete the following table.
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Question No. 6
Find the missing angle.
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Question No. 7
Solve for x in each of the following.
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Question No. 8
Each interior angle of a regular polygon is 160°. How many sides does the polygon have?
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Question No. 9
Calculate the size of each interior angle of a regular heptagon.
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Question No. 10
A polygon is divided into seven triangles by drawing diagonals from one vertex.
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Question No. 11
A hexagon has three equal angles. The other three angles are 115°, 85° and 130°. What is the size of each of the three equal angles?
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Question No. 12
The figure below is a regular pentagon with centre O. Angle CÔD is called a central angle.
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Question No. 13
As the number of sides of a regular polygon increases, what happens to:
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Question No. 14
ABCDE is a regular pentagon. Calculate x.
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Question No. 15
The diagram shows a regular hexagon and a regular octagon. Calculate the size of the angle marked x.
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Question No. 16
Find the values of x, y and z in the following diagrams.
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Question No. 17
The length of a rectangular plot of land is 24 m. The distance between the opposite corners of the plot is 30 m. Calculate the breadth of the plot.
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Question No. 18
Calculate the length of the longest straight line which can be drawn on a rectangular white board which measures 2.5 m by 1.3 m.
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Question No. 19
A pole is tied to the ground by a rope as shown on the right-hand side. The rope is attached to the pole, 6 m above the ground, and at a point on the ground, 3.5 m from the foot of the pole. Calculate the length of the rope.
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Question No. 20
Give five examples of your own, of objects with horizontal and vertical surfaces.
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Question No. 21
Classify each of the three angles in the figure below as an angle of elevation, an angle of depression, or neither.
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Question No. 22
Show the angle of elevation and depression in each of the following.
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Question No. 23
A 5 m ladder rests against a tree on level ground and forms a 75° angle of elevation. Draw a diagram of the situation, indicating clearly the horizontal, the vertical and the angle of elevation.
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Question No. 24
A pilot travels at a height of 11 000 m above level ground. According to her GPS, she is 65 km away from the airport runway, as measured along the ground.
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Question No. 25
A dog, that is 8 m from the base of a tree, spots a squirrel in the tree at an angle of elevation of 40°. How tall is the tree?
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Question No. 26
A ship is on the surface of the water, and its radar detects a submarine at a distance of 72 m, at an angle of depression of 23°. At what depth below the surface of the water is the submarine?
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Question No. 27
Nagodeallah is 1.6 m tall and she is standing 10 m from a flagpole. If the angle of elevation is 25°, what is the height of the flagpole?
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Question No. 28
The diagram below shows a tower. From two points, 25 m apart, the angles of elevation to the top of the tower are 35° and 60°. Calculate the height of the building by using a scale drawing.
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Question No. 29
A man is standing 45 m away from a house. If the angle of elevation is 15°, what is the height of the house? Use a scale of 1 cm to 5 m to construct a scale drawing.
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Question No. 30
Two observers are looking up at the top of the same tree from two different points on the ground. The first observer, who is 25 m away from the base of the tree, looks up at an angle of elevation of 58°. The second observer is standing 15 m from the base of the tree. (Note: You may ignore the heights of the observers and assume their measurements are made directly from the ground.)
