<p>Hey you guys! </p>
<p>I need help on #35 on the real sat subject tests book for math ii c. The question is : "Figure 8 shows a triangle inscribed in a semicircle. What is the area of the triangle in terms of theta?"</p>
<p>and so like the picture is of a semicircle with diameter 2 and the angle extends from a part of the lower left circle .. touching and goes to the upper right of the circle so that two arcs are formed and yeah from that point, the line lowers back to the right most lower part to make a triangle. </p>
<p>lol i know the description is confusing but i dont get how to do it. the answer is 2sin(theta)cos(theta)</p>
<p>PLEASE HELP!</p>
<p>um..i plug in values:</p>
<p>make the angle theta = to 30* so the triangle becomes a 30-60-90, so you can label the sides 1, 2, and root(3)</p>
<p>now find the area of the triangle which comes out to be root(3)/2</p>
<p>and 2sin(30<em>)cos(30</em>) gives you root(3)/2</p>
<p>hope that helps.</p>
<p>You know that the triangle is a right triangle because of the way it's inscribed in a semicircle, so the longer leg is 2cos(theta) and the shorter leg is 2sin(theta) by definition.(hypotenuse times cos(theta) gives you the adjacent side length and hypotenuse times sin(theta) gives you the opposite side length). So, base times height divided by 2 gives you that answer.</p>
<p>ooohhh thanks you two! i get it now (:</p>