![]() And we use that information and the Pythagorean Theorem to solve for x. So this is x over two and this is x over two. ![]() Two congruent right triangles and so it also splits this base into two. The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known. So the key of realization here is isosceles triangle, the altitudes splits it into So this length right over here, that's going to be five and indeed, five squared plus 12 squared, that's 25 plus 144 is 169, 13 squared. This distance right here, the whole thing, the whole thing is So x is equal to the principle root of 100 which is equal to positive 10. But since we're dealing with distances, we know that we want the If the three side lengths of an isosceles triangle are given, then its area can be calculated using Heron’s formula. Learn more about, Area of Isosceles Triangle. Area of an Isosceles Triangle ½ × base × height. This purely mathematically and say, x could be The area of an isosceles triangle is equal to half the product of its base length and its height. Is equal to 25 times four is equal to 100. We can multiply both sides by four to isolate the x squared. So subtracting 144 from both sides and what do we get? On the left hand side, we have x squared over four is equal to 169 minus 144. ) Therefore the three sides are in the ratio. To find the ratio number of the hypotenuse h, we have, according to the Pythagorean theorem, h2 1 2 + 1 2 2. That's just x squared over two squared plus 144 144 is equal to 13 squared is 169. In an isosceles right triangle, the equal sides make the right angle. This is just the Pythagorean Theorem now. There are different formulas for a right-angled triangle, isosceles triangle, and equilateral triangle. The area of the triangle depends on the type of triangle. We can write that x over two squared plus the other side plus 12 squared is going to be equal to The formula for the area of the triangle can be expressed as Area A (b x h) square units, where h is the height of the triangle and b is the base of the triangle. We can say that x over two squared that's the base right over here this side right over here. Let's use the Pythagorean Theorem on this right triangle on the right hand side. And so now we can use that information and the fact and the Pythagorean Theorem to solve for x. So this is going to be x over two and this is going to be x over two. So they're both going to have 13 they're going to have one side that's 13, one side that is 12 and so this and this side are going to be the same. And since you have twoĪngles that are the same and you have a side between them that is the same this altitude of 12 is on both triangles, we know that both of these So that is going to be the same as that right over there. Because it's an isosceles triangle, this 90 degrees is the ![]() ![]() Is an isosceles triangle, we're going to have twoĪngles that are the same. Well the key realization to solve this is to realize that thisĪltitude that they dropped, this is going to form a right angle here and a right angle here and notice, both of these triangles, because this whole thing To find the value of x in the isosceles triangle shown below. ![]()
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