# Tajuk : Penyelesaian Segitiga

SOLUTION OF TRIANGLES

1.2 Use Sine Rule to find the unknown sides or angles of a triangle.

Task 1 : Find the unknown sides of a triangle when two of its angles and one of the corresponding

sides are known.

|(1) Diagram 1 shows the triangle ABC. |Answer : |

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| |[pic] |

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| |[pic] |

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| |Using the scientific calculator, |

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| |BC = 12.32 cm |

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|Calculate the length of BC. | |

|(2) Diagram 2 shows the triangle PQR | |

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|Calculate the length of PQ. |[ 8.794 cm ] |

|(3) Diagram 3 shows the triangle DEF. | |

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|Calculate the length of DE. | |

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| |[ 10.00 cm ] |

|(4) Diagram 4 shows the triangle KLM. | |

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|Calculate the length of KM. | |

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| |[ 11.26 cm ] |

|(5) Diagram 5 shows the triangle ABC. |Answer : |

| |[pic] |

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| |[pic] |

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| |[pic] |

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| |Using the scientific calculator, |

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| |AC = 11.56 cm |

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|Calculate the length of AC. | |

|(6) Diagram 6 shows the triangle PQR | |

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|Calculate the length of PR. | |

| |[ 6.527 cm ] |

|(7) Diagram 7 shows the triangle DEF. | |

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|Calculate the length of EF. | |

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| |[ 17.25 cm ] |

|(8) Diagram 8 shows the triangle KLM. | |

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|Calculate the length of KL. | |

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| |[ 16.26 cm ] |

Task 2 : Find the unknown sides of a triangle when two of its angles and the side not corresponding

to the angles are known.

|(9) Diagram 9 shows the triangle ABC. |Answer : |

| | |

| |[pic] |

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| |[pic] |

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| |[pic] |

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| |Using scientific calculator, |

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| |BC = 9.9996 cm or 10.00 cm |

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|Calculate the length of BC. | |

|(10) Diagram 10 shows the triangle ABC. | |

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|Calculate the length of AC. | |

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| |[ 4.517 cm ] |

|(11) Diagram 11 shows the triangle PQR. | |

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|Calculate the length of PQ. | |

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| |[ 3.810 cm ] |

|(12) Diagram 12 shows the triangle DEF. | |

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|Calculate the length of DE. | |

| |[ 5.189 cm ] |

Task 3 : Find the unknown angles of a triangle when two sides and a non-included angle are given.

|(1) Diagram 1 shows the triangle ABC. |Answer : |

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| |[pic] |

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| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

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|Find (ACB. | |

|(2) Diagram 2 shows the triangle KLM | |

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|Find (KLM | |

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| |[ 27.360 ] |

|(3) Diagram 3 shows the triangle DEF. | |

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|Find (DFE. | |

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| |[ 11.090 ] |

|(4) Diagram 4 shows the triangle PQR. | |

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|Find (QPR. | |

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| |[ 36.110 ] |

|(5) Diagram 5 shows the triangle ABC. |Answer : |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

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|Find (ABC. | |

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|(6) Diagram 6 shows the triangle KLM. | |

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|Find (KLM. | |

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| |[ 138.640 ] |

|(7) Diagram 7 shows the triangle DEF. | |

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|Find (DFE. | |

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| |[ 124.460 ] |

|(8) Diagram 8 shows the triangle PQR. | |

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|Find (PQR. | |

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| |[ 94.150 ] |

Task 4 : Find the unknown side of a triangle when two sides and a non-included angle are given.

|(1) Diagram 1 shows the triangle ABC. |Answer : |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

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|Given that (ACB is an obtuse angle, find |AC = 8.018 cm |

|the length of AC. | |

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|(2) Diagram 2 shows the triangle KLM | |

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|Given that (KLM is an obtuse angle, find | |

|the length of ML. | |

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| |[ 2.952 cm ] |

|(3) Diagram 3 shows the triangle DEF. | |

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|Given that the value of (EDF is greater than | |

|900, find the length of DE. | |

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| |[ 5.040 cm ] |

|(4) Diagram 4 shows the triangle PQR. | |

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|Given that (PQR is an angle in the second | |

|quadrant of the cartesian plane, find the | |

|length of QR. | |

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| |[ 2.707 cm ] |

|(5) Diagram 5 shows the triangle KLM. | |

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|Given that (KLM is an angle in the second | |

|quadrant of the cartesian plane, find the | |

|length of KL. | |

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| |[ 9.686 cm ] |

-----------------------

Diagram 12

[pic]

Diagram 1

5.6 cm

[pic]

Diagram 2

D

E

F

600

350 16’

15 cm

Diagram 3

Diagram 4

15 cm

630

420

M

K

L

510

720

F

E

D

Diagram 11

7.2 cm

280

250

Q

P

R

[pic]

Diagram 10

Diagram 9

Diagram 5

9.2 cm

230

17.3 cm

M

K

L

Diagram 4

8.5 cm

460

6.9 cm

Q

P

R

Diagram 3

8 cm

420

11 cm

F

E

D

Diagram 2

9 cm

400

7 cm

M

K

L

9 cm

Diagram 1

14 cm

370

C

A

B

7.7 cm

Diagram 8

12.3 cm

550

Q

R

P

4.4 cm

Diagram 7

6.7 cm

340

F

D

E

Diagram 6

2.8 cm

250

4.2 cm

M

K

L

9 cm

Diagram 5

14 cm

1100

C

A

B

Diagram 4

13 cm

1300

10 cm

Q

P

R

Diagram 3

12.5 cm

430 24’

3.5 cm

F

E

D

Diagram 2

15 cm

500

9 cm

M

K

L

10 cm

Diagram 1

15 cm

600

C

B

To find unknown angles :

[pic]

To find unknown sides :

[pic]

A

[pic]

Diagram 5

[pic]

Diagram 6

D

E

F

600

350 16’

15 cm

Diagram 7

L

K

M

420

630

15 cm

Diagram 8

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