How can you know if this equation is true? 1/3+1/5=2/8=1/4
1 answer:
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Answer:
b = 25m
Step-by-step explanation:
Hi there!
We're given angle B and the length of <em>a</em> in this right triangle. We must solve for the length of <em>b</em>. <em>a</em> and <em>b</em> are the two legs of the right triangle.
In this case, we can use the tangent ratio:
Plug in the given information:
Therefore, b = 25m.
We can also use this using special triangle rules. radians is equal to 45 degrees, making this a 45-90-45 triangle. This would make <em>a</em> and <em>b</em> equal in length.
I hope this helps!
Recall that sine is the ratio of opposite over hypotenuse, so we say
sin(theta) = opposite/hypotenuse
If we have a triangle labeled as such in the diagram below, then we can use symbols to write sin(theta) = A/C
Similarly, cos(theta) = B/C since cosine is the ratio of adjacent over hypotenuse.
Then from here we use a bit of algebra to compute the left hand side of the given equation. The goal is to see if we can simplify it to 1.
So this shows that the left hand side is identically the same as the right hand side (both sides are 1), and it doesn't matter what you replace theta with. Theta can be any real number and the equation will always be true.
Note: if you're wondering how A^2+B^2 became C^2, it's because of the pythagorean theorem. So that's why this trig identity is often referred to as the pythagorean trig identity.
