Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. the angle of elevation of the tree from one position on a flat path from the tree is upper h equals 30 degrees commah=30°, and from a second position upper l equals 50 feetl=50 feet farther along this path it is upper b equals 20 degrees .b=20°. what is the height of the tree?

Please find the attached diagram for a better understanding of the solution provided here.

In the attached diagram, OP is the height of the tree.

Rest of the diagram should be sufficiently self explanatory.

In ,

.........................Equation #1

Again, in ,

.........................Equation #2

Thus, equating the equations Equation #1 and Equation #2, we have:

Evaluating we get:

Thus the height of the tree is approximately 49.26 feet

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: