The hypotenuse of a right-angled triangle is 20 cm, and the projection of the cosine
| June 16, 2021 | education
The hypotenuse of a right-angled triangle is 20 cm, and the projection of the cosine of one of the acute angles is 0.8. find the leg of this triangle.
1. Vertices of the triangle A, B, C. ∠C = 90 °. Cosine ∠A = 0.8.
2. Find the length of the AC leg through the cosine ∠A – the ratio of the AC leg, which is a side of this angle to the hypotenuse AB:
AC / AB = cosine ∠A = 0.8.
AC = AB x 0.8 = 20 x 0.8 = 16 centimeters.
3. Calculate the length of the BC leg. For the calculation, we use the formula of the Pythagorean theorem:
BC = AC = √AB² – AC² = √20² – 16² = √400 – 256 = √144 = 12 centimeters.
Answer: AC = 16 centimeters, BC = 12 centimeters.
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