Find the sides of a right-angled triangle if you know that its hypotenuse is 10 cm

Find the sides of a right-angled triangle if you know that its hypotenuse is 10 cm and one acute angle is 2 times larger than the other.

First, find the sharp corners of this triangle. Since one angle is twice as large as the other angle, we will express them as follows:

x = angle ∠B;

2x – the value of the angle ∠A;

90 ° is the degree measure of the angle ∠С;

180 ° = the sum of all the angles of the triangle;

x + 2x + 90 = 180;

3x = 180 – 90 = 90;

x = 90/3 = 30;

∠В = 30 °;

∠А = 2 30 = 60 °.

Using the sine of an acute angle, you can find the side of the AC:

sin B = AC / AB;

AC = AB sin B;

sin 30 ° = ½;

AC = 10 ½ = 5 cm.

Now, according to the Pythagorean theorem, you can find the length of the second leg:

AB ^ 2 = BC ^ 2 + AC ^ 2;

BC ^ 2 = AB ^ 2 – AC ^ 2;

BC ^ 2 = 10 ^ 2 – 52 ^ = 100 – 25 = 75;

BC = √75 = 8.66 cm.

Answer: the legs of the triangle are 5 cm and 8.66 cm.