The ratio of the projections of the legs to the hypotenuse of a right triangle is 0.25.
July 29, 2021 | education|
The ratio of the projections of the legs to the hypotenuse of a right triangle is 0.25. Find the length of the height drawn from the top of the right angle if the length of the hypotenuse is 20cm.
Let’s introduce a variable.
Let m be the length of the projection of one leg of a right-angled triangle, then (4 * m) is the projection of the second leg onto the hypotenuse.
Let’s find the projections of the legs:
m + 4 * m = 20;
m = 4;
4 * m = 16;
We use the Pythagorean theorem for two triangles formed by the height:
a ^ 2 = h ^ 2 + 16;
b ^ 2 = h ^ 2 + 256;
Now we use the Pythagorean theorem for the big triangle:
(5 * m) ^ 2 = a ^ 2 + b ^ 2;
400 = h ^ 2 + 16 + h ^ 2 + 256;
2 * h ^ 2 = 400 – 272;
2 * h ^ 2 = 128;
h ^ 2 = 64;
h = 8 cm.
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