Question

1. Write the measures of its sides in ascending
order in each of the following triangles :
(1) In A ABC, ZA= 50° and B = 60°
(2) In A PQR. ZP = 40° and R = 80°
(3) In A XYZ, X = 80º and Y= 30°
( 4 ) In A ABC, B = 70° and C= 20°
(5) In A POR. P = 93° and R = 55°​

Answer 1

Step-by-step explanation:

Angle C =180°-(40°+60°) =80°. , longest side is c as angle C is the largest angle.

By sine rule:-

a/sinA. = b/sinB = c/sinC.

or, a/sin 40° = b/sin 60° = c/sin80°.

Now, a/sin40° = c/sin80°.

or, c = a.sin80°/sin 40° = a.(2.sin 40°.cos40°)/sin40°. = 2a.cos40°.

or, c = 2a.cos 40°. …………………(1)

Also , b/sin60° = c/sin80°.

or, c = b.sin 80°/sin 60°. = (2b/√3).sin 80°…………….(2)

From eqn. (1) and (2).

Longest side c. = 2a.cos40° or , (2b/√3).sin 80°.