![]() So by applying the trigonometric formula for the area of a triangle, we found that the area of this isosceles triangle to three decimal places is 644.190 square centimeters. The units for this area are square centimeters. As the digit in the fourth decimal place is a two, we round down to 644.190. In this article, we explain: What an isosceles triangle is How to calculate the third side of an isosceles triangle and How to calculate the sides of an isosceles right triangle from the hypotenuse. The question specifies that we should give our answer to three decimal places. FAQ Welcome to the isosceles triangle side calculator, where we'll learn all there is to know about an isosceles triangle's sides. And we can then evaluate this on a calculator, ensuring that it is in degree mode. That gives 1152 multiplied by sin of 34 degrees. We have that the area is equal to a half multiplied by 48 multiplied by 48 multiplied by sin of 34 degrees. ![]() So we can substitute these values into the trigonometric formula for the area of a triangle. We now know the lengths of two sides in this triangle and the measure of their included angle. We have 180 degrees minus 73 degrees minus 73 degrees, which is 34 degrees. So we can calculate the measure of the third angle by subtracting the measures of the other two, the two base angles, from 180 degrees. We know that the angles in any triangle sum to 180 degrees. We don’t yet know the measure of their included angle, but we can work it out. Returning to the isosceles triangle in this question, we are given the lengths of two sides, the two equal sides of the isosceles triangle, which are each of length 48 centimeters. That’s the angle between the two side lengths □ and □. And the uppercase □ represents the measure of their included angle. The letters □ and □ represent the lengths of any two sides in the triangle. If we have a triangle □□□, where the uppercase letters □, □, and □ represent the vertices of the triangle and the lowercase letters □, □, and □ represent the side lengths opposite each of these angles, the area of this triangle is given by the formula a half □□ sin □. We can recall the trigonometric formula for the area of a triangle. But there is in fact a more straightforward way to find the area of this triangle. We could calculate each of these values using trigonometry. But in this problem, we don’t know either the base or the perpendicular height of this triangle. Now, usually, we might find the area of a triangle using the formula base multiplied by perpendicular height over two. We’re asked to find the area of this triangle. The base angles, which are the angles between each of these sides and the third side of the triangle, are each 73 degrees. So these are the two sides of equal length. ![]() We’re told that it is an isosceles triangle and it has two sides of length 48 centimeters. Find the area of the triangle, giving the answer to three decimal places. It is the 2 sides which are opposite the 2 equal base angles which are equal in length.An isosceles triangle has two sides of length 48 centimeters and base angles of 73 degrees. Make sure that you get the equal sides and angles in the correct position. The common mistake is identifying the wrong sides as the equal (congruent sides). Seeing the triangles in different positions will help with this understanding.įor example, here is a picture where the base angles of an isosceles triangle are on the top. The common mistake is thinking that the base of the angles are always on the bottom of the isosceles triangle. ![]() So when students classify the triangles, they wind up classifying them incorrectly. However, equilateral triangles have three equal (congruent) sides and angles and can be classified as isosceles.Ī common mistake when classifying triangles is mixing up the definitions of acute angle and obtuse angle. Isosceles triangles only have two equal (congruent) sides and angles and cannot be classified as equilateral. Understanding that properties of isosceles triangles and equilateral triangles can help with questions like this. The easy mistake to make is stating that isosceles triangles can be classified as equilateral triangles. Thinking that isosceles triangles can be classified as equilateral trianglesĪ question may ask students to explain if an isosceles triangle can be equilateral. ![]()
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