two vertical cliffs are on opposite sides of a 90 foot wide river. From point A at the top of the shorter cliff, the angle of el
evation of the top of the other cliff(b) is 28 degress and the angle of depression to the bottom is 38 degress.find the height of each cliff ,to the nearest foot
Answer: The tall cliff is 118.20 feet tall and the short cliff is 70.32 feet tall.
If you draw a picture with 2 cliffs and a river in the middle, you have find 2 right triangles. In each triangle the adjacent side to our known angle is the river of 90 feet. And the unknown side is the opposite leg.
Therefore, we can set up a tangent equation.
From the top of the short cliff to the top of the tall cliff, we can right and solve the following trig equation:
tan(28) = x /90 x = 47.88
From the top of the short cliff to the bottom, we can right and solve the following trip equation.
tan(38) = x/90 x = 70.32
The 70.32 is also the height of the short cliff. And adding the two answers together will give you the height of the tall cliff.
<span>It will take Yanni 20 minutes to catch up with Tracy. This can be determined with the fact that average velocity equals change in distance divided by change in time. Rearrange the equation so that we are solving for the final time, then set Tracy's equation equal to Yanni's equation and solve for the final time.</span>
