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math trigonometry

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From on point on the ground the angle of elevation to the peak of a mountain is 10.38 degrees and from another pont 15,560 feet closer to the mountain, the anle of elevation is 14.67 degrees. Both point are due south of the mountain. What is the height of the mountain? My answer is 41512 ft. Can someone confirm my answer or help with the correct one.

You may want to recheck your answer. The one I got, at least if I understand the question correctly, is 9,491 ft. I used the law of sines 15560/sin 4.29 =x/sin 14.67. Then I used sin 14.67 * x = height to get the answer.

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