A rhombus has 25-cm sides, and one diagonal is 14 cm long. How long is the other diagonal?
1 answer:
Let's visualize this problem (See the picture below). The red line represents the diagonal that is 14 cm, the green sides represent the 25-cm sides, and the yellow line represents the diagonal that we need to find. From this, you can see that the Pythagorean Theorem can be applied to this problem (Since the diagonals are perpendicular)
a^2+b^2=c^2
14^2+b^2=25^2
196+b^2=625
b^2=429
b=20.71 (approximate)
:)
a^2+b^2=c^2
14^2+b^2=25^2
196+b^2=625
b^2=429
b=20.71 (approximate)
:)
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Answer:
cos(θ) = 3/5
Step-by-step explanation:
We can think of this situation as a triangle rectangle (you can see it in the image below).
Here, we have a triangle rectangle with an angle θ, such that the adjacent cathetus to θ is 3 units long, and the cathetus opposite to θ is 4 units long.
Here we want to find cos(θ).
You should remember:
cos(θ) = (adjacent cathetus)/(hypotenuse)
We already know that the adjacent cathetus is equal to 3.
And for the hypotenuse, we can use the Pythagorean's theorem, which says that the sum of the squares of the cathetus is equal to the square of the hypotenuse, this is:
3^2 + 4^2 = H^2
We can solve this for H, to get:
H = √( 3^2 + 4^2) = √(9 + 16) = √25 = 5
The hypotenuse is 5 units long.
Then we have:
cos(θ) = (adjacent cathetus)/(hypotenuse)
cos(θ) = 3/5
