11. Rocco and Biff are two koalas sitting at the top of two eucalyptus trees, which are
located 10 m apart, as shown. Rocco's tree
is exactly half as tall as Biff's tree. From
Rocco's point of view, the angle separating
Biff and the base of his tree is 70°. How high off the ground is each koala?

Biff's tree is 14 m off the ground and Rocco's tree is 7 m off the ground.

Step-by-step explanation:

Let the height of Biff's tree be represented by x, so that the height of Rocco's tree is .

Draw a straight line from Rocco's point of view to a point t to the middle of Biff's tree. This line divides x into two equal parts, and the angle is divided into each.

By alternate angle property,

Tan   =

= Tan   × 10

  = 7.00021

⇒       x = 2 × 7.0021

            = 14. 0042

         x = 14

Therefore, Biff's tree is 14 m off the ground and Rocco's tree is 7 m off the ground.

Biff height = 9.48m

Rocco's height= 4.74m

Step-by-step explanation:

As Rocco's tree is half as tall as Biff's tree, draw a horizontal line from Rocco on Rocco's tree which intersects the Biff's tree at he middle.

The angle 70 degrees is divided by 2 because of the horizontal line.

An upper right angle triangle is form by Rocco (point A), Midpoint of Biff's tree(point B), and Biff (point C).

As

where θ=35 and  base= 10m

As the perpendicular found is that of a triangle formed from midpoint of Biff's, to find the total height, multiply the found perpendicular with 2.

Biff height = 4.74*2 = 9.48m

Rocco's height is half of biff height

Rocco's height= 9.48/2 = 4.74m

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.

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