The tangent of an acute angle of a rectangular trapezoid is 0.2. Find its larger base if the smaller
| February 12, 2021 | education
The tangent of an acute angle of a rectangular trapezoid is 0.2. Find its larger base if the smaller base is equal to the height and equal to 9.
1. A, B, C, D – the tops of the trapezoid. BE – height. BC = BE = 9 units. ∠D = 90 °.
Tangent ∠A = 0.2.
2. We calculate the length of the segment AE through the tangent ∠A of the right-angled triangle ABE:
BE / AE = tangent ∠A = 0.2.
AE = 9: 0.2 = 45 units.
3. We calculate the length AD – the larger base of the trapezoid:
AD = AE + DE.
DE = BC = 9 units.
AD = 9 + 45 = 54 units.
Answer: the larger base of the trapezoid is 54 units.
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