Question

Mountain officials want to build a new ski lift from B to C as shown in the figure below. The distance from A to C is 1480 feet. They measure angle DAC to be 32 degrees and angle DBC to be 18 degrees. What is the distance A from to B? Round your answer to the nearest tenth of a foot.

Answer 1

Do you know how to find CD?

Answer 2

Do you know the definitions of sine cosine and tangent?

Answer 3

yes

Answer 4

Find the two sides that would form the ratio equivalent to sin(32deg)

Answer 5

how do I do that?

Answer 6

Find sin(32deg) using the definition

Answer 7

Hypotenuse is 1480

Answer 8

so I have to find the opposite ?

Answer 9

Yes

Answer 10

would it be 784.280564?

Answer 11

if so the hypotenuse CB is 2537.98496522845

Answer 12

what do i do now @kc_kennylau

Answer 13

@jdoe0001 can you help me with this?

Answer 14

have you covered the Law of Sines yet?

Answer 15

@jdoe0001 yes

Answer 16

The distance from A to B is 1158.66 ft rounded to the next foot 1159 ft? did i do this right @jdoe0001 @kc_kennylau @mathmale @whpalmer4

Answer 17

Looks like that is correct.

Answer 18

DA should be 1255.11 ft, and DA+AB = 2413.77 ft. tan 18 degrees = 784.281/(2413.77) so it all appears to be consistent.