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

part a

in a city ice cream is mostly only bought when the temperature is very high as ice cream cools down our

so we can derive the conclusion that as the temperature increases the number of ice creams sold also increases

part b

y intercept is 5

slope is 2

happy to

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