Triangle ABC is inscribed in a circle. AB is 12, AC is 6 and BC is 6 square root 3. Find arc BC.

These measures tell us that the triangle is a 30-60-90 triangle with a hypotenuse opposite the side AB and since we can see that arc BC is the arc of least measure, it must be 60 degrees

The perimeter of an equilateral triangle is 45 meters. find the length of an altitude.

which leads to 

The sides of an equilatersl triangle are 3x-1, 5y, and x+13. Find the measures of each side.

equilateral => 3x-1=x+13 => x=7

and x+7 turns into 7+13=20
and so all sides are 20 units

:)

In a ΔABC, angle B = 90 degrees, AB = 6 units and AC = 10 units then the length of angle bisector AD from angle A is

 cosA=6/10=3/5 

A=arccos(3/5) - about 53.13 deg
so half is about A2=26.57 deg
therefore
cosA2=6/AD
cos26.57=6/AD
AD=6/cos26.57=6.71

if the three sides of a triangle are 2, 5, and x units and area of triangle is x sq. units, what is the value of x ?

I used Heron's formula for the area and after some algebra we can see that there is no real solution for x:

IF AN OBTUSE TRIANGLE HAS A BASE OF 7 INCHES AND HEIGHT OF 10 INCHES WHAT IS THE AREA OF THE TRIANGLE ?

it is 35 square inches

In a 30-60-90 triangleABC with right angleB, and shortest leg lineAB=5, find the lengths of the other two sides" please and thank you.

AB=5
BC=10

find the area triangle of sides 5cm,6cm,7cm

where the semiperimeter is

 

a=5, b=6, c=7, s=18/2=9 

by substitution and simplification we get 
 


:)

Two sides of a triangle are twelve feet, what is the length of the third side?

Since we are only given two congruent sides, we cannot specify the length the third side. However we can describe what it must be... 

First off, our triangle must be isosceles and so the base angles must be congruent. Let's call the unknown side u and the angle between the congruent legs x, then the base angles must be: 

 

and so 

 
Next we can use the Law of Sines to find u 

 

but 
 

so we can write 



 


:)

How do I work out the height of a triangle when the angle of two sides are 45 degrees and 37 degrees?

Clearly we cannot specify the height without knowing any lengths of sides, but we can describe the relationship between the height, angle measures and side lengths: 



 


:)

Find, to the nearest square yard, the area of a triangular plot of ground that measures 15 yards by 20 yards by 25 yards.

We use Heron's formula: 
 


where 


 
Now a=15, b=20, c=25 



 



 



:)

In Triangle ABC, if angle A=60 degrees and angle B is greater than angle C, then the longest side is ?

The sum of the measures of a triangle is 180 degrees. If the measure of angle B is greater than that of B and they must sum to 120 degrees, then the measure of B must exceed 60 and so it must be the greatest

Find the area of triangle ABC to the nearest tenth if necessary. A= 35 degrees b=3 ft c= 7 ft

the area is found immediately by the formula:

which when calculated gives: A=6.0 square feet (when you check make sure your calculator is in degree mode)
:)

A triangle is such that its medium side is three times as long as its shortest side, and its longest side is five inches longer than four times its shortest side. The perimeter of the triangle is 69inches. Find the length of the medium side of the triangle

Solution:

First we decide on names for our sides: 

s-short side
m-medium
l-long 

Next let's look at each statement carefully... 

medium side is three times as long as its shortest side means: 

 

longest side is five inches longer than four times its shortest side means: 

 

perimeter of the triangle is 69 inches means: 

 

Now we can substitute values: 

 

becomes 

 

Adding s-terms... 
 
 

so s=8 

Now