1. ABC is a right angled triangle where angle B is 90°. If angle C is 30° and side AC is 4m, then what is the measure of side AB?
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Correct answer is option - 1
Explanation: Given angle C = 30°. So, sin(C) = (opposite side)/ (hypotenuse).
This implies, sin(C) = AB/AC ==>sin(30°) = AB/4.
This gives: side AB = 4 sin(30°) = 4 * 1/2 = 2m
2. ABC is a right angled triangle where angle B is 90°. If angle C is 30° and side AC is 5m, then what is the measure of side BC?
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Correct answer is option - 3
Explanation: Given angle C = 30°. So, cos(C) = (adjacent side)/ (hypotenuse).
This implies, cos(C) = BC/AC ==>cos(30°) = BC/5.
This gives: side BC = 5 cos(30°) = 4.33m
3. PQR is a right triangle with right angle at vertex Q. If angle P is 45° and side QR is 3m, then what is the length of side PQ?
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Correct answer is option - 2
Explanation: Given angle P = 45°. So, tan(P) = (opposite side)/ (adjacent side).
This implies, tan(P) = QR/PQ ==> tan(45°) = 3m/PQ.
This gives: side PQ = 3 tan(45°) = 3m.
4. In a right triangle ABC with right angle at vertex B, if side AB is 2√3m and side BC is 2m, then what is the measure of angle C?
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Correct answer is option - 3
Explanation:To find angle C we can use, tan(C) because the opposite side AB and adjacent side BC measures are given.
This implies: tan(C) = (opposite side)/(adjacent side) -> tan(C) = AB/BC.
This gives: tan(C) = 2√3/ 2 ==> tan(C) = √3.
This means, angle C = tan^{-1}(√3) ==> angle C = 60°.
5. PQR is a right triangle with right angle at vertex Q. If angle P is 60° and side PR is 7m, then what is the length of side PQ?
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Correct answer is option - 4
Explanation: Given angle P = 60°. So, cos(P) = (adjacent side)/ (hypotenuse).
This implies, cos(P) = PQ/PR ==>cos(60°) = PQ/7.
This gives: side PQ = 7 cos(60°) = 3.5m