In triangle ABC, ∠B= 30∘, ∠C=45∘. If CD = 8 cm, then AB is equal to
16 cm
In ΔADC, ∠ACD=45∘,∠DAC=180−(90∘+45∘)=45∘
Therefore, angles of △ADC are 45∘,45∘,90∘
⇒sin(45):sin(45):sin(90)
⇒1√2:1√2:1
⇒1:1:√2
Therefore, the corresponding sides will be in the ratio 1:1:√2
45∘45∘90∘1:1:√2↓↓↓ADDCAC↓↓↓8 cm8 cm8√2 cm
AD = 8 cm
Now, in triangle ABD ∠A= (180∘−90∘−30∘)= 60∘.
Therefore, angles of triangle ABD are 30∘,60∘,90∘
Hence, the corresponding sides will be in the ratio 1:√3:2
30∘60∘90∘1:√3:2↓↓↓ADBDAB↓↓↓8 cm8√3 cm16 cm
Hence, AB =16 cm