SAT Trigonometry Problem!

Today we’ll be solvingĀ a practice SAT trigonometry problem and walking you through the steps to solve it!

Trig Problem

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 theĀ 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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