Question

16. If the angles of a triangle are 30°,
45° and the included side is
(V3 + 1), then what is the area of
the triangle ?
(a) (13+1) cm2 (b)2(V3+1) cm?
(c) (43+2) cm2 (d)) (1334) cm​

Answer 1

Answer:

(√3 + 1)/2 cm²

Step-by-step explanation:

angles of a triangle are 30°,  45° and the included side is  (√3 + 1)

Let say ΔABC

AB = √3 + 1  & ∠A = 30°  & ∠B = 45°

CD⊥AB

Tan ∠A = CD/AD

=> Tan 30° = CD/AD

=> 1/√3 = CD/AD

=> AD = CD√3

Tan ∠B = CD/BD

=> Tan 45° = CD/BD

=> 1 = CD/BD

=> BD = CD

AB = AD + BD = CD√3 + CD = CD  (√3 + 1)

AB = √3 + 1

=> CD  (√3 + 1)  = √3 + 1

=> CD = 1

Area of ΔABC = (1/2) * AB * CD

= (1/2)(√3 + 1)*1

= (√3 + 1)/2 cm²

the area of  the triangle = (√3 + 1)/2 cm²