Show every step for problems (a) - (c) * = this symbol means equal distant Solve
ID: 3183974 • Letter: S
Question
Show every step for problems (a) - (c)
* = this symbol means equal distant
Solve #2 2. (a) Prove that in a triangle, there can be at most one obtuse angle. (b) Prove that if both ZB and ZC are acute, then the altitude from A to Lsc intersects the latter at a point D so thatB*D*C. (c) Suppose LA in ABC is Prove that the altitude from B or C intersects the opposite side at a point no belonging to the side; more precisely, if the altitude from B to LAc intersec the latter at E, then C A E, and similarly for the altitude from C 288 Show transcribed image textExplanation / Answer
(a)Sum of all angles of a triangle is 180o. As all angles are positive and obtuse angle is >90o Sum of two obtuse angles will exceed the limit.
(b) If D lies outside BC then(assuming B-C-D, for other case just B and C will interchange in answer.) Then angle BAD> angle BAC>90o and angle ADB is 90o. Thus sum of them will exceed 180o which is not possible as BAD is a triangle. As angle is smaller BD<BC (sine rule)
(c) Angle BAC+ Angle BCA+ angle ABC=180o. In triangle BEC, angle BEC+ angle BCE+ angle CBE=180o. Now angle A > angle E and angle C is common. Thus CBE>ABC as sum is 180 in both cases.
As angle is greater CE>AC.(sine rule)