Dragan

In triangle $ABC$, we have $\angle A = 30^\circ$, $\angle B = 60^\circ$, and $\angle C=90^\circ$. Point $X$ is on $\overline{AC}$ such that $\overline{BX}$ bisects $\angle ABC$. If $AB = 12$, then what is the area of triangle $ABX$?

 Area of the triangle  ABX = ( AB/2) * [( AB/2) * tan(A)] 

                                    Area   ABX ≈ 20.785 u²  

One angle of a triangle is three times as large as another. The measure of the third angle is 65 more than the smallest angle. What are the measures of each angle?

(180-65) /5 = 23        angles are:  69,   23,  and 88  

There are 3 radii:  r=10,  r=7, r=3  

Two sides of an acute triangle measure 33 units and 65 units. Which is a possible length for the third side? 

a = 33        b = 65       

Side  'c'  should be longer then 56 but shorter then 72.89718787  

A rectangular building is 4 meters by 6 meters. A dog is tied to a rope that is 10 meters long, and the other end is tied to the midpoint of one of the long sides of the building. Find the total area of the region that the dog can reach (not including the inside of the building), in square meters.

Total area is  248.1858196 m²  

A family buys a car for $20,000. The value of the car decreases about 20% per year. After 6 years, the family decides to sell the car. Should they sell it for $4,000? Explain

Car value today is $ 20,000

year

1st         20,000    -20%   = 16,000

2nd        16,000    -20%   = 12,800

3rd         12,800    -20%   = 10,240

4th          10,240   -20%   =  8,192

5th          8,192     -20%   = 6,553.6

6th          6,553.6   -20%   = 5,242.88

In right triangle ABC with the right angle at vertex A, altitude AE is drawn from vertex A to hypotenuse BC, AE = 21, and CE = 20. Find the length of BC. Round your answer to the nearest hundredth.

Triangles  ABC, ACE and ABE  are similar.

AE = 21

CE = 20

Angle ACB = ?              tan(ACB) = AE / CE        ∠ ACB = 46.397°

BE = tan(BAE) * AE           BE = 22.05

BC = CE + BE           BC = 42.05  

Impressive!!!  

The length of a rectangle is 3 more than its width. The perimeter of the rectangle is 58 cm. What are the rectangle’s dimensions?

( 58 - 2*3) / 4 = 13            Rectanle sides are:  a = 13cm   b = 16cm  

Keith buys 3 kiwis and 4 zucchini's for a total of $4.95. A Kiwi costs $0.25 more than a zucchini. What is the cost of 1 kiwi and 1 zucchini?

(4.95 - 3*0.25) / 7 = 0.6           Zucchini costs 60 cents  and  kiwi costs 85 cents.

                                              Therefore, the cost of  1 kiwi and 1 zucchini is $ 1.45