Solution of Right Angled Triangles

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To solve a right angled triangle, we need to find out the unknown sides and the angles with the help of t-ratios.

To find a side, usually we take such t-ratios that involve the unknown sides.

In the figure, AB = 100 cm, find (i) x and (ii) y.

x = 0.7660 x 100

= 76.60 cm

y = 0.6428 x 100

= 64.28 cm.

In the figure, AC = 100 m, find (i) (ii) BC. Give your answer correct to the nearest metre.

90^o 89^o 60^'

44^o 36^'

45^o 24^'

= 45^o 24^'

1.0141

BC = 100 x 1.0141

BC = 101.41

We have taken ÐA because, the side opposite to A is the unknown side. By this simple observation, we have done multiplication instead of division during calculations.

To find height of a Triangle

(a) When the altitude falls within the base.

In DABC,  AD is its height. Let AD = h and BC = a.

Prove that

In DABC,

In DACD,

BC = BD + DC

(b) When the altitude falls outside the base

In DABC, ÐACB is obtuse.

BC = a and AD = h.

Proceeding as in (a) above, we can prove that

In DABC, ÐB = 42^o 36', ÐC = 50^o 12' BC = 100 m. Find AD.Using (where a is the base)

= 52.05

In the figure, ÐACD = 50^o, ÐB = 33^o 54' BC = 100 m. Find AD.

AD = 154 m