Problem

Problem

In ΔABC\Delta ABC , ADAD is an altitude from AA on side BCBC . If b>cb > c , ∠C=23∘\angle C = 23^\circ and AD=abcb2−c2AD = \frac{abc}{b^2 - c^2} , then ∠B\angle B is a. 110∘110^\circ b. 113∘113^\circ c. 120∘120^\circ d. 130∘130^\circ
Intuitive explanation

The key is recognizing that the altitude ADAD creates two right triangles where you can express ADAD in terms of the sides and angles. Since you're given a specific formula for ADAD in terms of aa, bb, cc, you need to derive what ADAD equals using basic trigonometry, then equate it to the given expression to find a relationship between the angles. The constraint b>cb > c and the given angle ∠C=23°\angle C = 23° will pin down ∠B\angle B uniquely.

Intuitive explanation

The key is recognizing that the altitude ADAD creates two right triangles where you can express ADAD in terms of the sides and angles. Since you're given a specific formula for ADAD in terms of aa, bb, cc, you need to derive what ADAD equals using basic trigonometry, then equate it to the given expression to find a relationship between the angles. The constraint b>cb > c and the given angle ∠C=23°\angle C = 23° will pin down ∠B\angle B uniquely.

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