A zipline is constructed over a ravine as shown in the diagram at the right. What is the horizontal distance from the bottom of the ladder to the platform where the zipline ends? Round your answer to the nearest tenth of a foot.

X= 284.04

To solve for x, you must first find the missing angle in the left corner. I will name it "< Y" (Angle Y)

2

Sin50/250 = SinY/60

Set up your problem, then cross multiply.

3

60(Sin50)= 250(Sin Y)

60(Sin50)/250= Sin Y

After cross multiplying, you should be left with this. You then cancel out 250 by dividing it on both sides to get Sin Y by itself.

4

Sin Y = 0.183

Y= Sin-1 x 0.183

This is what it solves out to.

Now you cancel out Sin on both sides, and it should look like the bottom problem.

5

Y= 10.5

This is now your answer to plug into the problem needed to solve for X.

6

Now because you have 2 out of 3 angles, you can solve for the missing angle that lays opposite to x. ( in SOHCAHTOA you need the OPPOSITE and the HYPOTENUSE. The Hypotenuse is originally give, but we had to do extra solving to find the Opposite's degree.)

7

Because degree's in a triangle add to 180, we will add 50 degrees + 10.5 degrees to get 60.5 degrees. Now subtract 60.5 from the full 180 degrees and we get 119.5 degrees as the missing number that lays opposite from X. Now we can solve for X.

8

(Sin 119.5)/x = (Sin 50)/250

Set up your final problem as so and cross multiply.

9

X(Sin 50) = 250(Sin 119.5)

X = 250(Sin119.5)/(Sin50)

After cross multiplying, the problem should look like the one at the top. Cancel out Sin 50 to get X by itself by dividing both sides by Sin 50, then solve for X.

Step-by-step explanation:

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