What is the area of this triangle?

enter your answer as a decimal in the box. round only your final answer to the nearest tenth.

13.2

Step-by-step explanation:

First we find the missing side of the triangle using the law of cosines:

c² = a²+b²-2ab(cos C)

c² = 8²+7²-2(8)(7)(cos 28)

c² = 64+49-112(cos 28)

c² = 113-112(cos 28)

c² = 14.1099

√c² = √14.1099

c = 3.8

Next we use the law of sines to find the angle opposite the 7 cm side:

sin 28/3.8 = sin B/7

Cross multiply:

7(sin 28) = 3.8(sin B)

Divide both sides by 3.8:

7(sin 28)/3.8 = 3.8(sin B)/3.8

0.8648 = sin B

Take the inverse sine:

sin⁻¹(0.8648) = sin⁻¹(sin B)

60 = B

The height of the triangle will extend from the lowest vertex to the 8 cm side.  This makes the right triangle formed to the left a 30-60-90 triangle.  In these triangles, the side opposite the 90 degree angle is twice as much as the side opposite the 30 degree angle; this means the portion of the 8 cm side from the height to the left will be 3.8/2 = 1.9 cm.

Using the Pythagorean theorem with 1.9 as a leg and 3.8 as the hypotenuse,

1.9² + b² = 3.8²

3.61 + b² = 14.44

Subtract 3.61 from each side:

3.61 + b² - 3.61 = 14.44 - 3.61

b² = 10.83

Take the square root of each side:

√b² = √10.83

b = 3.3

This means the height of the triangle is 3.3.  Using 8 as the base,

A = 1/2bh

A = 1/2(3.3)(8) = 13.2

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct