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9. Convert 37.952° to degrees and minutes. 0.952° = 0.952 × 60′ = 57.12′ = 57′ to the nearest minute Hence, 37.952° = 37° 57′ This answer can be obtained using the calculator as follows: 1. Enter 37.952 Press = 3. Press ° ’ ’ ’ Answer = 37° 57′ to the nearest minute 10. Convert 58.381° to degrees, minutes and seconds. 0.381° = 0.381 × 60′ = 22.86′ 0.86′ = 0.86 × 60′′ = 52′′ to the nearest second Hence, 58.381° = 58° 22′ 52′′ This answer can be obtained using the calculator as follows: 1. Enter 58.381 2. Press = 3. Press ° ’ ’ ’ Answer = 58° 22′ 51.6′′
1. State the general name given to an angle of 197°. 197° is an example of a reflex angle 2. State the general name given to an angle of 136°. 136° is an example of a obtuse angle 3. State the general name given to an angle of 49°. 49° is an example of a acute angle 4. State the general name given to an angle of 90°. 90° is a right angle 5. Determine the angles complementary to the following:
(a) 69° (b) 27°37′ (c) 4l°3′43′′
(a) The angle complementary 69° is: 90° – 69° = 21°
Angle a = 69° (vertically opposite angles) Angle b = 90° – 69° = 21° (angles in a right angle add up to 90°) Angle c = 180° – 29° – 69° = 82° (angles on a straight line add up to 180°) 11. Find angle β in the diagram.
In the diagram below, DEF is parallel to GH and ABC, and ∠CBE = 180° – 133° = 47°
In Figure (a), angle a = 180° – 83° – 57° = 40° In Figure (b), angle c = 180° – 114° = 66° and angle b = 180° – 32° – 66° = 82° In Figure (c), angle d = 180° – 105° = 75° angle f = 180° – 105° = 75° and angle e = 180° – 75° – 75° = 30° 3. In the triangle DEF which side is the hypotenuse? With reference to angle D, which side is the adjacent?
The hypotenuse is the longest side in a right-angled triangle and is the side opposite the right angle. Hence, the hypotenuse is side DF The side opposite angle D is EF; thus the adjacent side to angle D is the side DE 4. In triangle DEF of Problem 3, determine angle D. Angle D = 180° – 90° – 38° = 52° 5. MNO is an isosceles triangle in which the unequal angle is 65° as shown. Calculate angle θ.
If triangle MNO is isosceles, then ∠OMN = ∠MNO = 180 652° − ° = 57.5°
Hence, angle θ = 180° – 57.5° = 122.5° 6. Determine ∠φφ and ∠x in the diagram below.
∠DCE = 90° – 58° = 32° Hence, ∠ACB = 32° Then ∠ABC = 180° – 19° – 32° = 129° Thus, ∠φ = 180° – 129° = 51° and ∠x = 180° – 19° = 161° 7. In diagrams (a) and (b), find angles w, x, y and z. What is the name given to the types of
triangle shown in (a) and (b)?
In Figure (a), ∠x = ∠y = 180° – 110° = 70°
and ∠w = 180° – 70° – 70° = 40°
In Figure (b), the triangle is isosceles, with the two equal angles equal to 180 702° − ° = 55°
i.e. triangle PSX is right-angled, where SX = 9/2 = 4.5 cm Using Pythagoras, 2 2 2( ) ( ) ( )PS PX SX= + i.e. 2 2 29 ( ) (4.5)PX= + i.e. PX = 2 29 4.5− = 7.79 cm 3. In the diagram, find (a) the length of BC when AB = 6 cm, DE = 8 cm and DC = 3 cm,
(b) the length of DE when EC = 2 cm, AC = 5 cm and AB = 10 cm
(a) Triangle ABC is similar to triangle EDC. The two triangles are shown below side by side (not
to scale)
Thus, AB BCED DC
= i.e. 68 3
BC= from which, BC = 3 6
8× = 2.25 cm
(b) The two triangles are again shown below side by side (not to scale)