Two sides of an acute triangle measure 5 inches and 8 inches. the length of the longest side is unknown.
what is the greatest possible whole-number length of the unknown side?
8 inches
9 inches
12 inches
13 inches

Answer. 9 inches

1. Using some logical reasoning(Not proving because it will take a while) as the acute angle approaches to 90° the side in front of that angle extends.

2. Lets find the third side if the angle is 90° -> Using Pythagoras's theorem` hypotenuse(the side)=√(5*5+8*8) which is approximately 9.433 inches.

3. As we need to find the largest possible length of the unknown side its 9 inches, which is the biggest integer below 9.4.

Option 2 - 9 inches    

Step-by-step explanation:

Given : Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.

To find : What is the greatest possible whole-number length of the unknown side?

Solution :

Applying Pythagorean Theorem,

If c is the longest side of a acute triangle, a and b are other two sides of a acute triangle then the condition is given as,

We have given, P=5 , B=8

Substitute,

To the greatest possible whole number length of unknown side is 9 inches.

Therefore, Option 2 is correct.

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet