Mountain officials want to know the length of a new ski lift from a to c , as shown in the figure below. they measure angle dac to be 32° . they then move 960 feet to point b and measure angle dbc to be 18° . what is the length of the new ski lift from a to c ? round your answer to the nearest tenth of a foot.

We assume that the hill is represented by points ACD  and the ski lift is represented by points BCD. From the description above, points CDB would have an angle of 90 degrees. Then, we would have:

sin (32) = CD / 960
CD = 508.72

tan 32 = 508.72 / AD
AD = 814.13

Therefore, the distance would be 814.13 - 508.72 = 305.4 ft.

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