Swanson plans to attempt to swim across the lake from point A to point B as shown below. To determine how far he will have to swim, he has chosen a point C and calculated the labeled data. How many miles will he have to swim Round your answer to two decimal places.

Draw a perpendicular from C to AB. Let it touch at D. Let the angle ACD=x, BCD=y, We have x y=43.5=theta

Let h be the height. Now we have

h =AC cos x= BC cos y= BC cos (theta-x)=BC( cos theta cos x sin theta sin x)

This gives

cos x (AC-BC cos theta) = BC sin theta sin x

tan x = (AC BC cos theta)/(BCsin theta)=0.1

x=5.7

y=43.5-5.7=37.8

AD= AC sin (5.7)=0.84

BD= BC sin37.8=6.558

The total distance to swim is 6.558 0.84=7.398 miles.

You can follow this calculation to check this result.

This post is last updated on hrtanswers.com at Date : 1st of September – 2022