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Giải bài tập 10 trang 73 SGK Toán 9 tập 1 - Chân trời sáng tạo

Cho tam giác ABC vuông tại A có AB = 18 cm, AC = 24 cm. Tính các tỉ số lượng giác của góc B, từ đó suy ra các tỉ số lượng giác của góc C.

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

Toán - Văn - Anh
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Đề bài

Cho tam giác ABC vuông tại A có AB = 18 cm, AC = 24 cm. Tính các tỉ số lượng giác của góc B, từ đó suy ra các tỉ số lượng giác của góc C.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

-  Đọc kĩ dữ liệu đề bài để vẽ hình -  Áp dụng định lý Pythagore trong tam giác vuông để tính cạnh huyền -  Dựa vào tỉ số lượng giác của góc nhọn. Xét tam giác vuông: + Tỉ số giữa cạnh đối và cạnh huyền được gọi là sin, kí hiệu sin. + Tỉ số giữa cạnh kề và cạnh huyền được gọi là côsin, kí hiệu cos. + Tỉ số giữa cạnh đối và cạnh kề được gọi là tang, kí hiệu tan. + Tỉ số giữa cạnh kề và cạnh đối được gọi là côtang , kí hiệu cot. -  Dựa vào nếu hai góc phụ nhau thì sin góc này bằng cos góc kia, tan góc này bằng cot góc kia.

Lời giải chi tiết

Áp dụng định lý Pythagore trong tam giác ABC vuông tại A, ta có: BC = \(\sqrt {A{B^2} + A{C^2}}  = \sqrt {{{18}^2} + {{24}^2}}  = 30\) cm Các tỉ số lượng giác của góc \(\widehat B\) và \(\widehat C\) là: sin \(\widehat B\) = cos \(\widehat C\) = \(\frac{{AC}}{{BC}} = \frac{{24}}{{30}} = \frac{4}{5} =0,8\) cos \(\widehat B\) = sin \(\widehat C\) = \(\frac{{AB}}{{BC}} = \frac{{18}}{{30}} = \frac{3}{5} = 0,6\) tan \(\widehat B\) = cot \(\widehat C\) = \(\frac{{AC}}{{AB}} = \frac{{24}}{{18}} = \frac{4}{3} \approx 1,3\) cot \(\widehat B\) = tan \(\widehat C\) = \(\frac{1}{{\tan \widehat B}} = \frac{3}{4} = 0,75 \approx 0,8\)

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