But remember, we also defined angle □□□ to be equal to □. Simplifying eight-tenths by dividing both the numerator and denominator by two, and we see that eight-tenths is equivalent to four-fifths. In this case then, sin of □ must be equal to eight-tenths. And the hypotenuse, the longest side of our triangle, lies opposite the right angle. Well, side □□ sits directly opposite angle □. So we will be able to find the value of sin □□□ by dividing the opposite side to our included angle by the length of the hypotenuse. Now, of course, the trigonometric ratio for sin □ is opposite divided by hypotenuse. This means we can use right triangle trigonometry to find the value of sin of □. Then we notice that triangle □□□ is a right triangle for which we have an included angle we’re trying to find and we know two of the lengths. Since □ is the midpoint of □□, we can say that line segment □□ must be equal to eight centimeters. Then we can add this to our diagram as shown. So let’s begin by defining angle □□□ to be equal to □. Now we’re trying to find the value of sin of □□□. So we can deduce that line □□ must be perpendicular to line □□. Now, in fact, we know that if we bisect angle □□□ in our isosceles triangle, this angle bisector forms the line bisector of □□ as shown. We’re then told that □ is the midpoint of □□. And so perhaps triangle □□□ looks a little like this. These are shorter than the third side in the triangle □□. And the sides of equal length are □□ and □□. We know that □□□ is isosceles, in other words, two sides of equal length. Find the value of sin □□□ given that □ is the midpoint of □□.īefore we even try to find some trigonometric ratio, let’s begin by sketching out the triangle. □□□ is an isosceles triangle, where □□ equals □□, which equals 10 centimeters, and □□ equals 16 centimeters.
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