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Giải mục 1 trang 82, 83 SGK Toán 9 tập 1 - Cánh diều

Cho tam giác (ABC) vuông tại (A) (Hình 13). a) Biểu diễn (sin B,cos C) theo (AC,BC). b) Viết công thức tính (AC) theo (BC) và (sin B). c) Viết công thức tính (AC) theo (BC) và (cos C).

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

Toán - Văn - Anh
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HĐ1

Video hướng dẫn giải

Trả lời câu hỏi Hoạt động 1 trang 82 SGK Toán 9 Cánh diều

Cho tam giác \(ABC\) vuông tại \(A\) (Hình 13).

a) Biểu diễn \(\sin B,\cos C\) theo \(AC,BC\). b) Viết công thức tính \(AC\) theo \(BC\) và \(\sin B\). c) Viết công thức tính \(AC\) theo \(BC\) và \(\cos C\).

Phương pháp giải:

Dựa vào định nghĩa tỉ số lượng giác để giải bài toán.

Lời giải chi tiết:

a) \(\sin B = \frac{{AC}}{{BC}}\);\(\cos C = \frac{{AC}}{{BC}}\). b) \(AC = BC.\sin B\). c) \(AC = BC.\cos C\).

LT1

Video hướng dẫn giải

Trả lời câu hỏi Luyện tập 1 trang 83 SGK Toán 9 Cánh diều

Tính độ cao \(AC\) trong Hình 12 🤡khi \(BC = 20m\) (làm tròn kết quả đến hàng phần mười của mét)

 

Phương pháp giải:

Dựa vào quan hệ giữa cạnh huyền và tỉ số lượng giác của góc nhọn để tính.

Lời giải chi tiết:

Độ cao AC là: \(AC = BC.\sin 15^\circ  = 20.\sin 15^\circ  \approx 5,2\left( m \right)\).

LT2

Video hướng dẫn giải

Trả lời câu hỏi Luyện tập 2 trang 83 SGK Toán 9 Cánh diều

Cho tam giác nhọn \(ABC\) có đường cao \(CK\). Biểu thị \(CK\) theo \(AC\) và \(\sin A\). Từ đó, chứng minh diện tích tam giác \(ABC\) bằng \(\frac{1}{2}.AB.AC.\sin A\).

Phương pháp giải:

Dựa vào định nghĩ tỉ số lượng giác kết hợp với mối quan hệ giữa cạnh góc vuông, cạnh huyền và tỉ số lượng giác để giải bài toán.

Lời giải chi tiết:

Vì tam giác \(ACK\) vuông tại \(K\) nên: \(CK = AC.\sin A\).

Ta có: \({S_{ABC}} = \frac{1}{2}CK.AB = \frac{1}{2}.AB.AC.\sin A\).

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