30° and 60°.Further explanation
We will solve the problem of the measures of angles in the triangle.
Recall this condition:The acute angle ⇒ an angle of less than 90°.The right angle ⇒ an angle of exactly 90°.A right triangle ⇒ a triangle in which one angle is a right angle.The interior angles ⇒ the angles inside a triangle.All the interior angles in a triangle , i.e.,
The ratio of the measure of the acute angle in a right triangle is ¹/₂.
Find the measures of the two angles.
We call it the triangle ABC. An interior angle inside is a right angle, e.g., ∠A = 90°.
From the ratio of two other acute angles, i.e., 1: 2, we call it ∠B = x and ∠C = 2x.
Let's arrange the three angles in ABC triangle as follows:
Both sides subtracted by 90°.
Both sides divided by 3.
We substitute the value of x back into B and C.
We have succeeded in getting the measures of the two angles.Learn moreUndefined terms needed to define angles What is 270° converted to radians A triangle is rotated 90° about the origin
Keywords: the ratio, the measure, the acute angle, a right triangle, 1/2, 180°, 90°, 30°, 60°, the interior angles
The two acute angles of a right angled triangle are and .
It is given that the ratio of the measure of the acute angles of a right angled triangle is .
We know that for any triangle the summation of the all three angle is and as the triangle is right angled that means one angle is of and the other two angles are acute angles.
So the summation of the other two acute angle is .
Suppose the two acute angle is denoted as and . So in equation form it can be written as follows,
The ratio of the measure of the two acute angle is . This can be written in equation form as follows,
After rearranging the above equation we get,
Now substitute the above calculated value of in equation (1) to obtain the value of as follows,
Substitute this value of in equation (2) to obtain the value of as follows,
Therefore, the value of and is and respectively.
Thus, the two acute angles of a right angled triangle are and .
1. Problem on rules of transformation of triangles:
2. Problem on definition of an angle uses the undefined term:
3. Problem on the triangle to show on the graph with coordinates:
Grade: Middle School
Chapter: Angles and Triangles
Keywords: Angle, triangle, ratio, measure, right angled triangle, 30 degree, 60 degree, acute angle, summation, equation, rearrangement, 90 degree, perpendicular, vertical, horizontal, equation, value.
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