![]() ![]() ![]() The length of □□ is nine times the cos of 34 degrees. Finally, we can solve for the length of □□ by multiplying through by nine. We get the cos of 34 degrees is equal to the length of □□ divided by nine. Now, we can just substitute these values into this formula. We recall if □ is an angle in a right triangle, then the cos of □ is equal to the length of the side adjacent to angle □ divided by the length of the hypotenuse. Therefore, we need to use the cosine ratio. So, we know the length of the hypotenuse and we want to determine the length of the adjacent side. And we only know the length of the hypotenuse in this right triangle. We want to find the length of the line segment □□, and we’re doing this by finding the length of the line segment □□, which is our adjacent side. We’re now ready to apply our acronym to determine which of the trigonometric ratios we need to use. Finally, we can notice that side □□ is adjacent to this angle, so we label side □□ as the adjacent side. Next, we can see that the side □□ is opposite the angle 34 degrees, so we’ll label this as the opposite side. We can see that this is side □□ we’ll label this as the hypotenuse. We’re going to use triangle □□□.įirst, we’re going to label the hypotenuse as the longest side of the triangle, which is the one opposite the right angle. But first, we need to label the sides of our right triangle based on their position relative to the angle of 34 degrees. This will help us determine which of the three trigonometric ratios we need to use to determine the side length. To do this, we start by recalling the acronym SOH CAH TOA. We now want to apply right triangle trigonometry to determine the length of these two sides. However, we could’ve also showed this by using trigonometry. And in particular, this tells us the length of □□ is equal to the length of □□. Therefore, by the angle-angle-side congruence criterion, these two triangles are congruent. To do this, we first note that the triangles share two angles and the side length in common. We can notice that triangles □□□ and □□□ are congruent. ![]() However, there’s one extra simplification we can use. Adding these together would then give us the length of the line segment □□.Īnd this would work and give us the correct answer. Therefore, by using right triangle trigonometry, we could determine the length of line segment □□ and the length of line segment □□. And we recall if we know one of the non-right angles of a right triangle and one of the side lengths, we can use right triangle trigonometry to determine the other side length in the right triangle. However, the easiest way is to notice that □□□ and □□□ are both right triangles. There’s many different ways we can go about this. We need to give our answer to one decimal place. We need to use all of this information to determine the length of line segment □□. Therefore, the measure of angle □ is 34 degrees. ![]() And since the sides □□ and □□ have equal length, the measure of angle □ must be equal to the measure of angle □. But remember, this is an isosceles triangle. We’re also told that the measure of angle □ is 34 degrees. □□□ and □□□ are both right triangles with right angles at □. And we’re told that □□ is perpendicular to □□. In the diagram, we can also see that we have a line from □ to □, where □ is a point on the base of the triangle. First, we’re told that sides □□ and □□ have equal length. In this question, we’re given some information about an isosceles triangle □□□. Find the length of the line segment □□, giving the answer to one decimal place. □□□ is an isosceles triangle where the side □□ and the side □□ are equal to nine centimeters, the line segment □□ is perpendicular to the line segment □□, and the measure of angle □ is 34 degrees. ![]()
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