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![]() By substituting 10 for the length of the adjacent and □□ for the hypotenuse, we know then that cos of □ is equal to 10 over □□. Remember the cosine ratio tells us about the ratio between the adjacent and the hypotenuse. So that’s the side between the known angle and the right angle, in this case □□. The opposite is the side opposite the known angle. The hypotenuse and longest side of our right-angled triangle is the side directly opposite the right angle. Let’s label the three sides of the right-angled triangle □□□ in relation to angle □. Remember the definition of the cosine ratio in a right-angled triangle is that cos of a particular angle □ is equal to the length of the adjacent side divided by the length of the hypotenuse. We’re told that cos or cosine of the angle □ is equal to five over 13. ![]() So let’s look at the other piece of information given in the question. We still only know one length in each of these right-angled triangles. This means that the length of □□ 20 centimeters is divided exactly in half into two lengths of 10 centimeters. This means when I draw in a perpendicular height from the shared vertex of the two sides of equal length to the opposite side, this divides the triangle up into two identical right-angled triangles. ![]() And therefore, triangle □□□ is isosceles. The question tells us that two sides of the triangle □□ and □□ are the same length. In order to work out the area, we also need to know the perpendicular height of this triangle which I’m going to refer to as □□. In this question, we’ve only been given the length of one side of the triangle: □□ is 20 centimeters. The area of a triangle is found by multiplying its base by its perpendicular height and dividing by two. Find the area of triangle □□□, given that □□ is equal to □□, □□ is equal to 20 centimeters, and cos of □ is equal to five over 13.
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