In the triangle ABC, ABC = 105 and BAC = 30 Also, the length - Maths - Some Applications of Trigonometry

Question

​
In the triangle ABC, ∠ABC = 105° and ∠BAC = 30°
Also, the length of BC = 
cm

The area of ΔABC ?

Aman Choubey · Accepted Answer

Dear Student

BC is not mentioned in the question therefore we take it as 10 cm
Using Law of sines ABsinC =BCsinA ⇒AB= BC
sinCsinA=10
1122         ( angle C=180-(B+C) =45)⇒AB=10
2 cmNow Area of a Triangle with 2 angles and 1 included sides is given by  Area= 12
AB BC
sinB             =12
102 10
sin105             sin105 = sin(90+15)=cos15=cos(45-30)=cos45
cos30+sin45
sin30=3+122Therefore ,    Area = 12
102 10 3+122  Area = 253+1 sq  units
Regards

​ In the triangle ABC, ∠ABC = 105° and ∠BAC = 30°. Also, the length of BC = cm. The area of ΔABC ?

In the triangle ABC, ∠ABC = 105° and ∠BAC = 30°. Also, the length of BC = cm.

The area of ΔABC ?