Today we’ll be solving a practice SAT trigonometry problem and walking you through the steps to solve it!
If Sin(A)=0.5 and side BC=10, find the length of the hypotenuse, AB.
To set up this problem, we first need to think back to the definition of our trig functions. If you recall, the sine of an angle in a right triangle is defined as the opposite side over the hypotenuse, or
Given that Sin(A)=0.5, we can combine our two equations into
And with the knowledge that the side opposite of A has a length of 10, our equation now becomes
Moving h over gives us
and finally solving gives us
So our final answer is the hypotenuse, length AB, is 20 units long.
Bonus: What is the measure of angle A?
If you remember your special right triangles, you might notice that the relationship between one of our legs and the hypotenuse is 1:2, or in other words, this is one of our special right triangles, the 30-60-90 triangle!
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