15,如图,△ABC中,∠BAC:∠ABC=7:6 - 知识问答

15,如图,△ABC中,∠BAC:∠ABC=7:6,∠ABC比∠C大10°,BE,AD是△ABC的高,交于点H,求∠DH

1个回答

设∠ABC = 6x,则∠BAC = 7x,∠C = 6x-10°
∵AD⊥BC
∴∠ABC +∠BAD = 90°
∴∠BAD = 90°-6x
∴∠CAD = 7x-（90°-6x） = 13x-90°
∵∠CAD +∠C = 90°
∴ 13x-90°+6x-10°=90°
∴x = 10°
∴∠BAD = 30°
∠ABD=60°
∠C = 50°
∴∠EBC = 40°
∴∠ABE = 20°
∴∠BHD = ∠ABE+∠BAD = 20°+30° = 50
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