24 6.3 Math Lab: Constructing Triangles—Solutions DO NOT COPY. ©P

Lesson 6.3 Math Lab: Assess Your Understanding, pages 468–469

1. In �ABC, AB 4 cm and A 70°

a) Sketch a diagram to show that there are two triangles with BC 3.8 cm.

b) To the nearest degree, measure C for each triangle.

c) To the nearest hundredth of a centimetre, calculate the length ofBC for which �ABC is a right triangle.

2. In �ABC, AB 4 cm, BC = 3.5 cm, and A 70°Use the completed chart in Part D to justify that it is not possible to draw a triangle.

=∠=

∠

=

=∠=

AC1 C2

B

4 cm 3.8 cm

98°

70° 82°

C 98° or 82°�∠

If ABC is a right triangle, then

sin A

sin 70°

BC 4 sin 70°BC 3.7587. . .

To the nearest hundredth of a centimetre, BC 3.76 cm�

�

�

BC4�

�BCAB

¢

, or 0.875

sin 70° 0.940

Since sin 70°, then no triangle is possibleBCAB<

�

BCAB �

3.54

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256.3 Math Lab: Constructing Triangles—Solutions©P DO NOT COPY.

b) One right triangle is possible.

c) Two scalene triangles are possible.

b) Use the completed chart in Part D to justify that only one scalenetriangle can be drawn with the value you chose for BC.

4. In �ABC, AB 10 cm and BC 8 cm; to the nearest degree,determine possible measures of acute A for each situation.

a) No triangle is possible.

∠==

3. In �ABC, AB 4 cm and A 70°

a) Choose a value for BC for which a unique triangle that is not aright triangle can be drawn. Draw the triangle.

=∠=

4 cm 5 cm

A C

B

70°

Sample response: I chose BC 5 cm.

1.25

Since 1, then only one triangle is possibleBCAB>

�54�

BCAB

�

Sample response:

For two scalene triangles, sin A 1

0.8, so sin A 0.8

From part a, A 53°; so, for two scalene triangles, A 53°<∠<∠

<BCAB �

BCAB<<

For a right triangle, sin ASo, sin A 0.8From part a, A 53°; so, for one right triangle, A 53°�∠�∠

�

BCAB �

A is acute, so A 90°For no triangle, sin A , or 0.8

sin�1(0.8) 53°For an acute angle U, as U increases, sin U also increases.So, for no triangle, 53° A 90°<∠<

�

> 810

<∠∠

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