2.) matt is standing on top of a cliff 305 feet above a lake. the measurement of the angle of depression to a boat on the lake is 42 degrees . how far is the boat from the base of the cliff?

The boat is 338.7 feet away from the base of the cliff.

EXPLANATION

Let be the distance of the boat from the base of the cliff.

We can use alternate angles property to bring the angle of depression into the triangle.

Since the known side is opposite the angle and the sede we are finding is adjacent to it, we use the tangent ratio.

From the diagram,

Hence the boat is 338.7 feet away from the base of the cliff.

Using the concept of trigonometry, the distance of the boat from the base of the cliff is 338.74 feets

Recall :

Tan θ = opposite / Adjacent = height / base distance

Tan 42° = 305 / d

0.9004040 = 305 / d

d = 305 / 0.9004040

d = 338.74 feets.

Therefore, the distance from the base is 338.74 feets

Learn more : link

tickets for the harlem globetrotters

show at michigan state university in

2010 cost $16, $23, or, for vip seats, $40.

total revenue = 16x + 23y + 40z

if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, sales of all three kinds of tickets would

total $46,575.

16x + 23y + 40z = 46575, how many of each kind of ticket would

have been sold?

solve for x, y and z

x − 9z = 0

x − y − z = 55

16x + 23y + 40z = 46575

x = 1170

y = 985

z = 130

welcome!

step-by-step explanation: