Δ ABC, ∠ C=90, CH- высота , AB=26; tgB=5. AH = ?
Решение
1) 1 + tg²B = 1/Cos²B
1 + 25 = 1/Cos²B
26 = 1/Cos²B
Cos²B = 1/26
CosB = √26/26
2) Sin²B = 1 - Cos²B = 1 - 1/26 = 25/26
SinB = 5√26/26 = CosA
3) CA/AB = CosA
CA/26 = 5√26/26
CA = 5√26
4) AH/CA = CosA
AH = CA* CosA = 5√26* 5√26/26 = 25
5) ответ: AH = 25
Δ ABC, ∠ C=90, CH- высота , AB=26; tgB=5. AH = ?
Решение
1) 1 + tg²B = 1/Cos²B
1 + 25 = 1/Cos²B
26 = 1/Cos²B
Cos²B = 1/26
CosB = √26/26
2) Sin²B = 1 - Cos²B = 1 - 1/26 = 25/26
SinB = 5√26/26 = CosA
3) CA/AB = CosA
CA/26 = 5√26/26
CA = 5√26
4) AH/CA = CosA
AH = CA* CosA = 5√26* 5√26/26 = 25
5) ответ: AH = 25