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10.1E: Pembetatu zisizo za haki - Sheria ya Sines (Mazoezi)

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    Kwa mazoezi yafuatayo, kudhani\(\alpha\) ni kinyume upande\(a, \beta\) ni kinyume upande\(\mathbf{b},\) na\(\gamma\) ni kinyume upande\(c .\) Kutatua kila pembetatu, kama inawezekana. Pande kila jibu kwa kumi ya karibu.

    1. \(\beta=50^{\circ}, a=105, \mathbf{b}=45\)

    2. \(\alpha=43.1^{\circ}, a=184.2, \mathbf{b}=242.8\)

    3. Tatua pembetatu.

    Triangle na maandiko ya kawaida. Angle A ni digrii 36 na upande wa pili haijulikani. Angle B ni digrii 24 na upande wa pili b = 16. Angle C na upande c haijulikani.

    4. Pata eneo la pembetatu.

    Pembetatu. Pembe moja ni digrii 75 na upande wa kinyume haijulikani. Pande zilizo karibu na angle ya shahada 75 ni 8 na 11.

    5. Jaribio linaruka juu ya barabara kuu moja kwa moja. Anaamua pembe za unyogovu kwa mileposts mbili,\(2.1 \mathrm{~km}\) mbali, kuwa\(25^{\circ}\) na\(49^{\circ}\), kama inavyoonekana katika Kielelezo 1. Pata umbali wa ndege kutoka hatua\(A\) na mwinuko wa ndege.

    Mchoro wa ndege kuruka juu ya barabara kuu. Ni upande wa kushoto na juu ya pointi A na B juu ya ardhi kwa utaratibu huo. Kuna mstari usio na usawa unaopitia mpango unaofanana na ardhi. Pembe iliyoundwa na mstari wa usawa, ndege, na mstari kutoka ndege hadi kumweka B ni digrii 25. Pembe iliyoundwa na mstari usio na usawa, ndege, na uhakika A ni digrii 49.

    Kielelezo 1