A hot air balloon is 70 m above the sea. Two buoys A and B are due East of the balloon.
The angle of depression from the balloon to buoy A is 60°.
The angle of depression from the balloon to buoy B is 40°.
Calculate the distance AB. (Round to the nearest tenth.)

Step-by-step explanation:

in the rough drawing i've included we want to find the distance of AC and BC and the subtract the shorter from the longer  or

BC- AC = AB

does this strategy seem like a good one?

use the mnemonic SOH CAH TOA to remember how sin, cos, and tan, fit on a triangle

SOH     Sin = Opp / Hyp

CAH    Cos =Adj / Hyp

TOA   Tan = Opp / Adj

where Opp = Opposite side,  Adj = Adjacent side , and Hyp = Hypotenuse

we are given an angle and the Opposite side so we can use Tan , since that has the thing we want to find, and the things we know.

when  AC is the Adj side it's

Tan(60) = 70 / Adj

Adj = 70 / Tan(60)

Adj = 40.4145

Dist. of AC = 40.4145 m

When BC is the Adj side it's

Tan(40) = 70 / Adj

Adj = 70/ Tan(40)

Adj = 83.42275

Dist. of BC = 83.42275

BC - AC = AB

83.45575 - 40.4145 =43.008

to the nearest tenth  AB = 43.0 m

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1