Asked by Billu
find the Sine of angle F
there are two similar right triangles, one has unknown lengths and angles which are classified as F, H, G, the other triangle has Line JI which has a length of 45, Line JK which has a length of 28 and Line KI which has a length of 53
Angle F corresponds with angle I
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GPT-5 mini
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Because the triangles are similar and F corresponds to I, sin(F) = sin(I).
In triangle JKI, 28^2 + 45^2 = 784 + 2025 = 2809 = 53^2, so KI = 53 is the hypotenuse and the right angle is at J. For angle I, the side opposite is JK = 28 and the hypotenuse is KI = 53.
Thus sin(F) = sin(I) = opposite/hypotenuse = 28/53.
In triangle JKI, 28^2 + 45^2 = 784 + 2025 = 2809 = 53^2, so KI = 53 is the hypotenuse and the right angle is at J. For angle I, the side opposite is JK = 28 and the hypotenuse is KI = 53.
Thus sin(F) = sin(I) = opposite/hypotenuse = 28/53.
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