Question

if two angles of triangle are 30 and 45 and included side is√3+1 then area of triangle is​

Answer 1

Answer:

the area of  the triangle = (√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

Answer 2

Answer:

The Area of  the Triangle = $\frac{\sqrt{3} + 1}{2}$ cm²

Step-by-step explanation:

In this question,

We have been given that

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

Let say ΔABC

AB = √3 + 1  & ∠A = 30°  & ∠B = 45°

Let CD⊥AB

Tan ∠A = $\frac{CD}[AD}$

Tan 30° = $\frac{CD}{AD}$

$\frac{1}{√3}$ = $\frac{CD}{AD}$

AD = CD√3

Tan ∠B = $\frac{CD}{BD}$

Tan 45° = $\frac{CD}{BD}$

1 = $\frac{CD}{BD}$

BD = CD

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

AB = √3 + 1

CD  (√3 + 1)  = √3 + 1

CD = 1

Area of ΔABC = $\frac{1}{2}\times AB\times CD$

= $\frac{1}{2}\times (√3 + 1)\times 1$

= (√3 + 1)/2 cm²

The Area of  the Triangle = $\frac{\sqrt{3} + 1}{2}$ cm²