In the figure (1) given below, ∆ABC is isosceles with AB = AC = 5 cm and BC = 6 cm. Find (i) sin C (ii) tan B (iii) tan C - cot B.

Draw AD perpendicular to BC. D is the mid point of BC [∵ Perpendicular drawn to the unequal side of an isosceles triangle from the apex vertex bisects the side] So, BD = CD = 3 cm. In right-angled ∆ABD, Using pythagoras theorem we get : ⇒ AB 2 = AD 2 + BD 2 ⇒ AD 2 = AB 2 - BD 2 ⇒ AD 2 = 5 2 - 3 2 ⇒ AD 2 = 25 - 9 ⇒ AD 2 = 16 ⇒ AD = ⇒ AD = 4 cm. (i) In right-angled ∆ACD, sin C = = . Hence, sin C = . (ii) In right-angled ∆ABD, tan B = = . Hence, tan B = . (iii) In right-angled ∆ACD, tan C = = . In right-angled ∆ABD, cot B = = . Substituting values in tan C - cot B we get : Hence, tan C - cot B = .

In △PQR, ∠Q = 90°. If PQ = 40 cm and PR + QR = 50 cm, find :
(i) sin P
(ii) cos P
(iii) tan R

View Answer Bookmark Now

In △ABC, AB = AC = 15 cm, BC = 18 cm. Find
(i) cos ∠ABC
(ii) sin ∠ACB.

View Answer Bookmark Now

In the figure (2) given below, △ABC is right-angled at B. Given that ∠ACB = θ, side AB = 2 units and side BC = 1 unit, find the value of sin² θ + tan² θ.

View Answer Bookmark Now

Mathematics

In the figure (1) given below, ∆ABC is isosceles with AB = AC = 5 cm and BC = 6 cm. Find
(i) sin C
(ii) tan B
(iii) tan C - cot B.

Trigonometrical Ratios

Related Questions

In △PQR, ∠Q = 90°. If PQ = 40 cm and PR + QR = 50 cm, find :
(i) sin P
(ii) cos P
(iii) tan R

In △ABC, AB = AC = 15 cm, BC = 18 cm. Find
(i) cos ∠ABC
(ii) sin ∠ACB.

In the figure (2) given below, △ABC is right-angled at B. Given that ∠ACB = θ, side AB = 2 units and side BC = 1 unit, find the value of sin² θ + tan² θ.

Mathematics

In the figure (1) given below, ∆ABC is isosceles with AB = AC = 5 cm and BC = 6 cm. Find(i) sin C(ii) tan B(iii) tan C - cot B.

Trigonometrical Ratios

Related Questions

In △PQR, ∠Q = 90°. If PQ = 40 cm and PR + QR = 50 cm, find :(i) sin P(ii) cos P(iii) tan R

In △ABC, AB = AC = 15 cm, BC = 18 cm. Find(i) cos ∠ABC(ii) sin ∠ACB.

In the figure (2) given below, △ABC is right-angled at B. Given that ∠ACB = θ, side AB = 2 units and side BC = 1 unit, find the value of sin2 θ + tan2 θ.

In the figure (1) given below, ∆ABC is isosceles with AB = AC = 5 cm and BC = 6 cm. Find
(i) sin C
(ii) tan B
(iii) tan C - cot B.

In △PQR, ∠Q = 90°. If PQ = 40 cm and PR + QR = 50 cm, find :
(i) sin P
(ii) cos P
(iii) tan R

In △ABC, AB = AC = 15 cm, BC = 18 cm. Find
(i) cos ∠ABC
(ii) sin ∠ACB.

In the figure (2) given below, △ABC is right-angled at B. Given that ∠ACB = θ, side AB = 2 units and side BC = 1 unit, find the value of sin² θ + tan² θ.