The height of a right-angled triangle divides the right angle into two angles, one of which is 4 times larger than the other. find the sharp corners of the given triangle.
Let in a right-angled triangle the height drawn to the hypotenuse divides the right angle into two angles, one of which is 4 times larger than the other. Let’s find the degree measure of these angles.
Let the smaller angle be a, then the larger angle will be 4a, according to the property of the right angle, its degree measure = 90, then
a + 4a = 90
5a = 90
a = 90/5
a = 18, smaller angle
4a = 18 * 4 = 72, larger angle
By the property of similarity of triangles, the formed triangles are similar to each other and to the original triangle in two equal angles. This means that the larger acute angle of the original right-angled triangle is 72 degrees, and the smaller acute angle is 18 degrees.
Answer: 72 and 18
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