SKETCHING A TRIANGLE AND DETERMINE THE MEASURE OF INDICATED SIDE

Sketch each triangle. Determine the measure of the indicated side.

Example 1 :

In triangle ABC, ∠A = 57°, ∠B = 73°, and AB = 24 cm. Find the length of AC.

Solution :

AB  =  c  =  24 cm, BC  =  a, AC  =  b, <A  =  57 and <B  =  73

In triangle ABC,

<A + <B + <C  =  180

57 + 73 + <C  =  180

<C  =  180 - 130  =  50

Using sin formula,

a/sin A  =  b/sin B  =  c/sin C

a/sin 57  =  b/sin 73  =  24/sin 50

We have to solve for b.

Equating 1 and 3, we get

b/sin 73  =  24/sin 50

b/0.9563   =  24/0.7660

b  =  31.33(0.9563)

b  =  29.96

b  =  30 cm (approximately)

Hence the indicated side is 30 cm.

Example 2 :

In triangle ABC, ∠B = 38°, ∠C = 56°, and BC = 63 cm. Find the length of AB.

Solution :

AB  =  c, BC  =  a = 63, AC  =  b, <C  =  56 and <B  =  38

In triangle ABC,

<A + <B + <C  =  180

<A + 38 + 56  =  180

<A  =  180 - 94  =  86

Using sin formula,

a/sin A  =  b/sin B  =  c/sin C

63/sin 86  =  b/sin 38  =  c/sin 56

We have to solve for c.

Equating 1 and 3, we get

63/sin 86  =  c/sin 56

63/0.9975   =  c/0.8290

63.15  =  c/0.8290

c  =  63.15(0.8290)

c  =  52.35

c  =  52.4 cm (approximately)

Hence the indicated side is 52.4 cm.

Example 3 :

In triangle ABC, ∠A = 50°, ∠B = 50°, and AC = 27 m. Find the length of AB.

Solution :

AB  =  c, BC  =  a = 27 m,  AC  =  b = 27 m, <A  =  50 and <B  =  50

In triangle ABC,

<A + <B + <C  =  180

50 + 50 + <C  =  180

<C  =  180 - 100  =  80

Using sin formula,

a/sin A  =  b/sin B  =  c/sin C

27/sin 50  =  27/sin 50  =  c/sin 80

We have to solve for c.

Equating 1 and 3, we get

27/sin 50  =  c/sin 80

27/0.7660   =  c/0.9848

35.24  =  c/0.9848

c  = 35.24(0.9848)

c  =  34.70 m

Hence the indicated side is 34.7 m.

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