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Lý thuyết Một số hệ thức về cạnh và góc trong tam giác vuông Toán 9 Cánh diều

1. Tính cạnh góc vuông theo cạnh huyền và tỉ số lượng giác của góc nhọn Trong tam giác vuông, mỗi cạnh góc vuông bằng cạnh huyền nhân với sin góc đối hoặc nhân với côsin góc kề. Cạnh góc vuông = (cạnh huyền ) × (sin góc đối) = (cạnh huyền ) × (cosin góc kề)

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
Quảng cáo

1. Tính cạnh góc vuông theo cạnh huyền và tỉ số lượng giác của góc nhọn

Trong tam giác vuông, mỗi cạnh góc vuông bằng cạnh huyền nhân với sin góc đối hoặc nhân với côsin góc kề.

Cạnh góc vuông = (cạnh huyền ) × (sin góc đối)

= (cạnh huyền ) × (cosin góc kề)

Ví dụ 1:

Trong tam giác ABC vuông tại A, ta có:\(\begin{array}{l}b = a.\sin B = a.\cos C;\\c = a.\sin C = a.\cos B.\end{array}\)

2. Tính cạnh góc vuông theo cạnh góc vuông còn lại và tỉ số lượng giác của góc nhọn

Trong tam giác vuông, mỗi cạnh góc vuông bằng cạnh góc vuông kia nhân với tang góc đối hoặc côtang góc kề.

Cạnh góc vuông = (cạnh góc vuông còn lại ) × (tan góc đối) 

= (cạnh góc vuông còn lại ) × (cot góc kề)

Ví dụ 2:

Trong tam giác ABC vuông tại A, ta có:\(\begin{array}{l}b = c.\tan B = c.\cot C;\\c = b.\tan C = b.\cot B.\end{array}\)

3. Áp dụng tỉ số lượng giác của góc nhọn để giải tam giác vuông

Giải tam giác vuông là tìm tất cả độ dài các cạnh và số đo các góc còn lại của tam giác đó.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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