In a triangle ABC, angle C is 90, CH is the height, BC = 10, CH = 3√11. Find sin A.
| January 30, 2021 | education
1. Calculate the length of the HВ segment:
BH = √BC² – CH² (by the Pythagorean theorem).
HВ = √10² – (3√11) ² = √100 – 99 = 1 unit.
2. We calculate the length of the segment AH:
AH x BH = CH² (according to the properties of a right-angled triangle).
AH = CH²: BH = 99: 1 = 99 units.
3. AB = 99 + 1 = 100 units of measurement.
4. Sine ∠A = BC: AB = 10: 100 = 0.1.
Answer: sine ∠A is equal to 0.1.
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