Question

in a right angle triangle angle B=90° and angle A is twice angle C. find angle C full process
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Answer 1

Answer:

Step-by-step explanation: GIVEN➡BCA=2BAC---------------1.)

In ∆ABC

➡angle BCA+ angle CBA + angle BAC = 180°

➡2 angle BAC + 90 + angle BAC = 180° [ from-1 ]

➡3 angle BAC = 90°

➡angle BAC = 90/3

➡angle BAC=30° and BCA=2×30=60°

Better use trigonometry

➡sin30=BC/AC

➡1/2=BC/AC

➡AC=2BC

(proved)

Answer 2

Given : In a right angle triangle, ∠B = 90° and ∠A is twice ∠C.

To Find : Measure of ∠C?

Solution :

Let,

• The measure of ∠C be x.
• The measure of ∠A be 2x.

As we know,

$\bf{\fbox{Sum \: of \: angles \: of \: triangle = 180°}}$

$\mathfrak{ \therefore \: \angle A + \angle B + \angle C = 180°}$

$\sf{ \mapsto \: 2x + 90° + x = 180°}$

$\sf{ \mapsto \: 3x = 180° - 90°}$

$\sf{ \mapsto \: x = \dfrac{ \cancel{90°} }{ \cancel{3} } }$

$\sf{ \mapsto \: x = 30°}$

Hence,

• The measure of ∠C is 30°.
• The measure of ∠A is (30° × 2) = 60°.