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Answers
Given
- ABC is a right angle∆ where ∠C = 60° , right angled at B
- AC = 10 cm
To Find
- Value of ∠A
- Length of BC
- Perimeter of the triangle
Solution
☯ ∠A can be found using the angle sum property
☯ BC can be found using the cos function
☯ Perimeter of the triangle can be found after we find BC using tan function and then add up the function
★ ∠A of the ∆ABC
→ ∠A + ∠B + ∠C = 180°
→ ∠A + 90° + 60° = 180°
→ ∠A + 150° = 180°
→ ∠A = 180-150
→ ∠A = 30°
★ Length of BC
→ cos θ = Hypotenuse/Adjacent
→ cos 60° = 10/BC
→ ½ = 10/BC
→ BC = 10 × 2
→ BC = 20 cm
★ Length of AC [To find Perimeter]
→ tan θ = Opposite/Adjacent
→ tan 60° = AB/20
→ √3 = AB/20
→ AB = 20√3
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Perimeter of the Triangle
→ Perimeter = 10+20+20√3
→ Perimeter = 30+20√3
→ Perimeter = 10(3+2√3) cm
Answer:-
Option (d), a) 30° b) 5 cm c) 15 + 5√3 cm
Given:-
- Measure of ∠B = 90°
- Measure of ∠C = 60°
- AC = 10 cm
To find:-
a.) Measure of ∠A
b.) Length of BC
c.) Perimeter of triangle ABC
Explanation:-
a.) We know that the sum of interior angles of a triangle is 180°,
⇒ ∠A + ∠B + ∠C = 180°
⇒ ∠A + 90° + 60° = 180°
⇒ ∠A = 180° – 150°
⇒ ∠A = 30°
Thus, the measure of ∠A is 30°.
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b.) Sin A = P/H
Sin 30° = BC/AC
Sin 30° = BC/10
1/2 = BC/10
10/2 = BC
BC = 5cm.
Thus, the length of BC is 5 cm.
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c.) Using pythagoras theorem,
AC² = BC² + AB²
AB² = AC² – BC²
AB² = 10² – 5²
AB² = 100 – 25
AB² = 75
AB = √75 cm
AB = 5√3 cm.
Perimeter of the △ABC = Sum of all sides
= AC + BC + AB
= 10 + 5 + 5√3
= 15 + 5√3
Thus, the perimetre of △ABC is 15 + 5√3 cm.
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Therefore, option (d), a) 30° b) 5 cm c) 15 + 5√3 cm is correct.