Number 75: Find the length of side x.

Step-by-step explanation:

Unless you know that the top angle is a right angle (an assumption you should never make, but I will do it here because there is no other way to do it.)

Find the missing side of the triangle that is on the bottom triangle

b^2 = c^2 - a^2

b = ?

c = 11

a = 10

b^2 = 11^2 - 10^2

b^2 = 121 - 100

b = sqrt(21)

Now using the fact that

b / 10 = 10 / (x - b)          

We know b from the previous problem

b = sqrt(21)

So now cross multiply

b ( x - sqrt(21) ) = 100

sqrt(21) * x - 21 = 100         Add 21 to both sides.

sqrt(21)x = 121                   Divide by sqrt(21)

x = 121/sqrt(21)

x = 26.4

My first inclination is to tell your teacher it is unsolvable. Or you can ask him or her to show you how it is done.  If they think the assumption I have made is correct, then you have the answer. Technically however, there is no answer.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

answer: 4 (:

step-by-step explanation: