In the right triangle shown, what is the cosine of angle C?
2 answers:
The cos(C) = 
we first need to find the actual lengths of the sides.. to do this we will use the Pythagorean theorem:
(x + 15)² + (x + 1)² = (x + 17)² and now after simplifying both sides and moving everything to one side we get the following quadratic equation:
x² - 2x - 63 = 0 and solving by factoring we get solutions of x = 9 and x = -7, but x = -7 does not make sense in this problem.
Using x = 9 we see the sides of the triangle are 10, 24, and 26
the cos(c) =
which is about 0.9231
we first need to find the actual lengths of the sides.. to do this we will use the Pythagorean theorem:
(x + 15)² + (x + 1)² = (x + 17)² and now after simplifying both sides and moving everything to one side we get the following quadratic equation:
x² - 2x - 63 = 0 and solving by factoring we get solutions of x = 9 and x = -7, but x = -7 does not make sense in this problem.
Using x = 9 we see the sides of the triangle are 10, 24, and 26
the cos(c) =
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The image of the right rectangular prism is missing, so i have attached it.
Answer:
volume of the right rectangular prism = 625 in³
Step-by-step explanation:
The rectangular prism is made of equal-sized cubes. Thus, let's first find the volume of 1 cube.
Formula for volume of one cube is;
V = a³
where
a is the length of one side of the cube
We are told that this length is 2½ inches
Thus;
a = 2½ = 5/2 inches
>> V = (5/2)³
>> V = 125/8 in³
Now, in the rectangular prism attached, if we count the number of cubes we have, it is equal to 40 cubes
Therefore, the volume of the prism is;
Volume of one cube × 40
>> volume of the prism = (125/8) × 40
volume of the prism = 625 in³
