**Sketching a Triangle and Determine the Measure of Indicated Side :**

Here we are going to see some example problems based on finding the measure of indicated side by sketching a triangle.

**Question 1 :**

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

a) 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.

b) 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.

c) 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.

After having gone through the stuff given above, we hope that the students would have understood "Sketching a Triangle and Determine the Measure of Indicated Side".

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