WISKUNDE
GRAAD 10
NOG OEFENINGE
Trigonometriese toepassings.
GRAAD 10
NOG OEFENINGE
Trigonometriese toepassings.
MATHEMATICS
GRADE 10
MORE EXERCISES
Trigonometrical applications..
GRADE 10
MORE EXERCISES
Trigonometrical applications..
In hierdie oefening moet alle
antwoorde korrek tot 2
desimale gegee word,
tensy anders vermeld.
antwoorde korrek tot 2
desimale gegee word,
tensy anders vermeld.
should be given correct to
2 decimals unless
otherwise instructed.
In die diagram is ∠B = 38°,
∠C = 90° en BC = 7 cm.
In the diagram ∠B = 38°,
∠C = 90°and BC = 7 cm.
Bereken / Calculate
1.1 AB
1.2 AC
∠C = 90° en BC = 7 cm.
In the diagram ∠B = 38°,
∠C = 90°and BC = 7 cm.
Bereken / Calculate
1.1 AB
1.2 AC
In die diagram is ∠P = 43°,
∠Q = 90°en PQ = 8,2 cm.
In the diagram ∠P = 43°,
∠Q = 90°and PQ = 8,2 cm.
Bereken / Calculate
2.1 PR
2.2 QR
∠Q = 90°en PQ = 8,2 cm.
In the diagram ∠P = 43°,
∠Q = 90°and PQ = 8,2 cm.
Bereken / Calculate
2.1 PR
2.2 QR
In ΔKLM is ∠L =90°,
KL = 6 cm, en KM = 7,3 cm.
In ΔKLM ∠L =90°,
KL = 6 cm, and KM = 7,3 cm.
Bereken / Calculate
3.1 ∠K
3.2 ∠M
KL = 6 cm, en KM = 7,3 cm.
In ΔKLM ∠L =90°,
KL = 6 cm, and KM = 7,3 cm.
Bereken / Calculate
3.1 ∠K
3.2 ∠M
In ΔPQR is ∠Q = 90°,
PQ = 12 cm en QR = 6,3 cm.
In ΔPQR is ∠Q = 90°,
PQ = 12 cm and QR = 6,3 cm.
Bereken / Calculate
4.1 ∠P
4.2 ∠R
PQ = 12 cm en QR = 6,3 cm.
In ΔPQR is ∠Q = 90°,
PQ = 12 cm and QR = 6,3 cm.
Bereken / Calculate
4.1 ∠P
4.2 ∠R
In ΔPQR is ∠Q = 90°,
∠P = 38°, PS = 15 cm
en QS ⊥ PR.
In ΔPQR ∠Q = 90°,
∠P = 38°, PS = 15 cm
and QS ⊥ PR.
Bereken / Calculate
5.1 QS
5.2 SR
5.3 ∠ RQS
∠P = 38°, PS = 15 cm
en QS ⊥ PR.
In ΔPQR ∠Q = 90°,
∠P = 38°, PS = 15 cm
and QS ⊥ PR.
Bereken / Calculate
5.1 QS
5.2 SR
5.3 ∠ RQS
In ΔPQR is ∠Q = 90°, ∠PRS = 90°,
∠PRQ = 41°, ∠SPR = 28°
en SR = 12 cm.
In ΔPQR ∠Q = 90°, ∠PRS = 90°,
∠PRQ = 41°, ∠SPR = 28°
and SR = 12 cm.
Bereken / Calculate
6.1 PR
6.2 PQ
6.3 oppervlakte van / area of ΔPQR
∠PRQ = 41°, ∠SPR = 28°
en SR = 12 cm.
In ΔPQR ∠Q = 90°, ∠PRS = 90°,
∠PRQ = 41°, ∠SPR = 28°
and SR = 12 cm.
Bereken / Calculate
6.1 PR
6.2 PQ
6.3 oppervlakte van / area of ΔPQR
In die figuur is ∠B = 90°,
∠D = 32°, ∠ACB = 48°
∠en CD = 24 cm.
In the figure ∠B = 90°,
∠D = 32°, ∠ACB = 48°
, and CD = 24 cm.
Bereken / Calculate
7.1 BC
7.2 AB
7.3 AD
∠D = 32°, ∠ACB = 48°
∠en CD = 24 cm.
In the figure ∠B = 90°,
∠D = 32°, ∠ACB = 48°
, and CD = 24 cm.
Bereken / Calculate
7.1 BC
7.2 AB
7.3 AD
In die figuur stel AB 'n leer, 8 m lank,
wat teen 'n muur, AC, leun, voor.
Die leer maak 'n hoek van 62° met
die vloer EBC.
In the figure AB represents a ladder,
8 m long, that rests against a wall, AC.
The ladder forms an angle of 62°
with the floor EBC.
Bereken / Calculate
wat teen 'n muur, AC, leun, voor.
Die leer maak 'n hoek van 62° met
die vloer EBC.
In the figure AB represents a ladder,
8 m long, that rests against a wall, AC.
The ladder forms an angle of 62°
with the floor EBC.
Bereken / Calculate
8.1 Hoe hoog reik die leer teen die muur? /
At what height does the ladder touch the wall?
8.2 Die bopunt van die leer sak nou 1,5 m. Wat is die grootte van die hoek tussen
die leer en die vloer? /
The top of the ladder is lowered by 1,5 m. What angle does the ladder make
with the floor?
At what height does the ladder touch the wall?
8.2 Die bopunt van die leer sak nou 1,5 m. Wat is die grootte van die hoek tussen
die leer en die vloer? /
The top of the ladder is lowered by 1,5 m. What angle does the ladder make
with the floor?
Bestudeer die figuur. Van die bopunt van
'n krans, AC, 63 m, hoog, is die
dieptehoek na 'n boot op die
see 35°. Hoe ver is die boot van die
krans af?
Study the figure. From the top of a cliff,
AC, 63 m high, the angle of depression to
a boat on the sea is 35°. How far is
the boat from the cliff?
'n krans, AC, 63 m, hoog, is die
dieptehoek na 'n boot op die
see 35°. Hoe ver is die boot van die
krans af?
Study the figure. From the top of a cliff,
AC, 63 m high, the angle of depression to
a boat on the sea is 35°. How far is
the boat from the cliff?
Vanaf 'n boot op die see, B, is die
hoogtehoek na die bopunt van 'n
vuurtoring, AC, 30°. Die vuurtoring is
69,6 m hoog. Die boot vaar nou nader na
die vuurtoring en vanaf punt D is die
hoogtehoek nou 54,3°. Watter afstand,
tot die naaste meter, het die boot tussen
die twee waarnemings gevaar?
From a boat at sea, B, the angle of
elevation to the top of a lighthouse, AC,
hoogtehoek na die bopunt van 'n
vuurtoring, AC, 30°. Die vuurtoring is
69,6 m hoog. Die boot vaar nou nader na
die vuurtoring en vanaf punt D is die
hoogtehoek nou 54,3°. Watter afstand,
tot die naaste meter, het die boot tussen
die twee waarnemings gevaar?
From a boat at sea, B, the angle of
elevation to the top of a lighthouse, AC,
is 30°. The lighthouse is 69,6 m high. The boat now sails closer to the lighthouse
and from point D the angle of elevation is now 54,3°.What distance, to the nearst metre,
did the boat sail between the two observations?
and from point D the angle of elevation is now 54,3°.What distance, to the nearst metre,
did the boat sail between the two observations?
In die figuur is
∠Q = ∠PRS = ∠TPS = 90°,
∠RPQ =32°, ∠PSR = 65°,
∠TPS = 40° en TP = 8 eenhede.
In the figure
∠Q = ∠PRS = ∠TPS = 90°,
∠RPQ =32°, ∠PSR = 65°,
∠TPS = 40° and TP = 8 units.
Bereken / Calculate
11.1 PS
11.2 RQ
∠Q = ∠PRS = ∠TPS = 90°,
∠RPQ =32°, ∠PSR = 65°,
∠TPS = 40° en TP = 8 eenhede.
In the figure
∠Q = ∠PRS = ∠TPS = 90°,
∠RPQ =32°, ∠PSR = 65°,
∠TPS = 40° and TP = 8 units.
Bereken / Calculate
11.1 PS
11.2 RQ
Vanaf 'n punt B is 'n man regoor punt A
op die oorkantste oewer van 'n rivier.
Vanaf punt B stap hy nou 100 m langs
die oewer van die rivier na punt C.
Vanaf C vind hy dat die hoek na
punt A 40,38° is. Maak 'n skets om
die gegewens voor te stel en
bereken dan die breedte van
die rivier, AB.
op die oorkantste oewer van 'n rivier.
Vanaf punt B stap hy nou 100 m langs
die oewer van die rivier na punt C.
Vanaf C vind hy dat die hoek na
punt A 40,38° is. Maak 'n skets om
die gegewens voor te stel en
bereken dan die breedte van
die rivier, AB.
From a point B a man is exactly opposite
point A on the opposite bank of a river.
From point B he now walks 100 m on the
river bank to point C. From C he finds
that the angle to point A is 40,38°.
Draw a figure to represent the facts and
then calculate the breadth of the
river, AB.
point A on the opposite bank of a river.
From point B he now walks 100 m on the
river bank to point C. From C he finds
that the angle to point A is 40,38°.
Draw a figure to represent the facts and
then calculate the breadth of the
river, AB.
In die figuur stel AC 'n gebou voor.
Punte B, C en D is almal in dieselfde
horisontale vlak.Vanaf punt D, 20 m
vanaf C, is die hoogtehoek na die bopunt
van die gebou, AC, 40,4°
In the figure AC represents a building.
Points B, C and D are all in the same
horizontal plane.From point D, 20 m
from C, the angle of elevation is 40,4°
Punte B, C en D is almal in dieselfde
horisontale vlak.Vanaf punt D, 20 m
vanaf C, is die hoogtehoek na die bopunt
van die gebou, AC, 40,4°
In the figure AC represents a building.
Points B, C and D are all in the same
horizontal plane.From point D, 20 m
from C, the angle of elevation is 40,4°
Bereken / Calculate
13.1 h, die hoogte van die gebou. / h, the height of the building.
13.2 x, die afstand BC. / x, the distance BC.
13.3 die afstand BD. / the distance BD.
13.1 h, die hoogte van die gebou. / h, the height of the building.
13.2 x, die afstand BC. / x, the distance BC.
13.3 die afstand BD. / the distance BD.
In die figuur stel DG 'n toring voor.
Punte E, F en G is almal in dieselfde
horisontale vlak.Vanaf punt F, 42 m
vanaf G, is die hoogtehoek na die
bopunt van die toring, D, 26,6° en
vanaf E is die hoogtehoek 16,7°.
In the figure AC represents a tower.
Points E, F and G are all in the same .
horizontal plane. From point F, 42 m
from G, the angle of elevation to the top
of the tower is 26,6° and from E the
angle of elevation is 16,7°.
Punte E, F en G is almal in dieselfde
horisontale vlak.Vanaf punt F, 42 m
vanaf G, is die hoogtehoek na die
bopunt van die toring, D, 26,6° en
vanaf E is die hoogtehoek 16,7°.
In the figure AC represents a tower.
Points E, F and G are all in the same .
horizontal plane. From point F, 42 m
from G, the angle of elevation to the top
of the tower is 26,6° and from E the
angle of elevation is 16,7°.
Bereken / Calculate
14.1 die hoogte van die toring. / the height of the tower.
14.2 die afstand DF. / the distance DF.
14.3 die afstand EG. / the distance EG.
14.1 die hoogte van die toring. / the height of the tower.
14.2 die afstand DF. / the distance DF.
14.3 die afstand EG. / the distance EG.
In die figuur stel PQ 'n diep kloof voor.
Punte P,Q, R en S is almal in dieselfde
horisontale vlak. Vanaf punt S, 75 m
vanaf R, is ∠QSR = 21,8°en
∠PSQ = 39,6°.
In the figure PQ represents a deep
canyon. Points P, Q, R and S are all in
the same horizontal plane.From point S,
75 m from R, ∠QSR = 21,8° and
∠PSQ = 39,6°
and ∠PSQ = 39,6°
Punte P,Q, R en S is almal in dieselfde
horisontale vlak. Vanaf punt S, 75 m
vanaf R, is ∠QSR = 21,8°en
∠PSQ = 39,6°.
In the figure PQ represents a deep
canyon. Points P, Q, R and S are all in
the same horizontal plane.From point S,
75 m from R, ∠QSR = 21,8° and
∠PSQ = 39,6°
and ∠PSQ = 39,6°
Bereken / Calculate
15.1 QR
15.2 QP
15.1 QR
15.2 QP
In die figuur stel ABDF die baan voor
wat 'n vliegtuig net na opstyging, teen
'n hoek van 10° volg. Die vliegtuig
vlieg teen 120 m.s-1
In the figure ABDF represents the path
that an aircraft follows after take off
at 10° The speed of the aircraft
is 120 m.s-1
wat 'n vliegtuig net na opstyging, teen
'n hoek van 10° volg. Die vliegtuig
vlieg teen 120 m.s-1
In the figure ABDF represents the path
that an aircraft follows after take off
at 10° The speed of the aircraft
is 120 m.s-1
Bereken / Calculate
16.1 Punt B word na 30 s bereik. Bepaal die hoogte van die vliegtuig. /
Point B is reached after 30 s. Determine the height of the aircraft.
16.2 Watter horisontale afstand, x, het dit bereik? /
What horizontal distance, x, is reached?
16.3 By D is die hoogte, DE, 833 m. Hoe lank neem dit die vliegtuig om die hoogte
te bereik? / At D the height, DE, is 833 m. How long after take off does the
aircraft reach this height?
16.4 By F is die hoogte, FG, 1 000 m. Watter horisontale afstand het die vliegtuig
nou afgelê? / At F the aircraft is 1 000 m high, FG. What horizontal distance
has it covered at this point?
16.1 Punt B word na 30 s bereik. Bepaal die hoogte van die vliegtuig. /
Point B is reached after 30 s. Determine the height of the aircraft.
16.2 Watter horisontale afstand, x, het dit bereik? /
What horizontal distance, x, is reached?
16.3 By D is die hoogte, DE, 833 m. Hoe lank neem dit die vliegtuig om die hoogte
te bereik? / At D the height, DE, is 833 m. How long after take off does the
aircraft reach this height?
16.4 By F is die hoogte, FG, 1 000 m. Watter horisontale afstand het die vliegtuig
nou afgelê? / At F the aircraft is 1 000 m high, FG. What horizontal distance
has it covered at this point?