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Giải bài tập 15 trang 105 SGK Toán 9 tập 1 - Chân trời sáng tạo

Hải đăng Kê Gà tọa lạc tại xã Tân Thành, huyên Hàm Thuận Nam, tỉnh Bình Thuận. Biết ngọn hải đăng cao 65 m so với mặt nước biển. Với khoảng cách bao nhiêu kilomet thì người quan sát trên tàu bắt đầu trông thấy ngọn của hải đăng này? Cho biết mắt người quan sát ở độ cao 5 m so với mực nước biển và bán kính Trái Đất gần bằng 6400 km.

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

Toán - Văn - Anh
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Đề bài

Hải đăng Kê Gà tọa lạc tại xã Tân Thành, huyên Hàm Thuận Nam, tỉnh Bình Thuận. Biết ngọn hải đăng cao 65 m so với mặt nước biển. Với khoảng cách bao nhiêu kilomet thì người quan sát trên tàu bắt đầu trông thấy ngọn của hải đăng này? Cho biết mắt người quan sát ở độ cao 5 m so với mực nước biển và bán kính Trái Đất gần bằng 6400 km.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng định lý Pythagore để tính AH và HB. Từ đó tính được AB = AH + HB.

Lời giải chi tiết

Ngọn của hải đăng là điểm \(A\) và mắt người quan sát ở vị trí \(B\). Khi người quan sát thấy ngọn hải đăng thì \(AB\) là tiếp tuyến của đường tròn \((O)\) tại \(H\). Suy ra \(OH \perp AB\) (tính chất của tiếp tuyến). Xét tam giác \(OAH\) vuông tại \(H\) có: \(OH \approx 6400\) (km); \(OA = AC + CO \approx 0,065 + 6400 = 6400,065 \text{ (km)};\) \(AH = \sqrt{OA^2 - OH^2} = \sqrt{(6400,065)^2 - 6400^2} \approx 28,84 \text{ (km)}.\) Xét tam giác \(OBH\) vuông tại \(H\), ta có: \(OB = BD + DO \approx 0,065 + 6400 = 6400,065 \text{ (km)};\) \(BH = \sqrt{OB^2 - OH^2} = \sqrt{(6400,065)^2 - 6400^2} \approx 28,84 \text{ (km)}.\) Ta có: \(AB = AH + HB \approx 28,84 + 8 = 36,84 \text{ (km)}.\) Vậy với khoảng cách khoảng 36,84 km thì người quan sát trên tàu bắt đầu trông thấy ngọn của hải đăng.

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

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