Question

In ABC, B = 90º, AC = 12 cm, BC = 6 cm. Find measure of A.

Answer 1

SOLUTION

GIVEN

In Δ ABC, ∠B = 90º, AC = 12 cm, BC = 6 cm.

TO DETERMINE

The measure of ∠A

EVALUATION

Here it is given that in Δ ABC, ∠B = 90º, AC = 12 cm, BC = 6 cm.

With the given information we construct the figure ( Refer to the attachment )

We have to determine ∠A

Now with respect to ∠A , BC is perpendicular and AC is hypotenuse

So

$\displaystyle \sf{ \sin A = \frac{BC}{AC} }$

$\displaystyle \sf{ \implies\sin A = \frac{6}{12} }$

$\displaystyle \sf{ \implies\sin A = \frac{1}{2} }$

$\displaystyle \sf{ \implies \: A = {30}^{ \circ} }$

Hence the required angle ∠A = 30°

FINAL ANSWER

The required angle ∠A = 30°

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Answer 2

TRIGONOMETRY

Given :-

A ∆ABC in which :-

∠B = 90°

AC = 12 cm

BC = 6 cm

To Find :-

Measure of ∠A

Solution :-

We will use trigonometric identities to solve this question.

We know that,

Sin A = Perpendicular/Hypotenuse.

Refer to the figure to check the values.

According to the figure, we have values of perpendicular and hypotenuse with respect to angle A.

Perpendicular = BC = 6 cm

Hypotenuse = AC = 12 cm

Put these values in the Sine formula,

Sin A = BC/AC

= 6/12

= 1/2

Sin A = 1/2

We know that at θ = 30°, the value of sine function is 1/2,

So, measure of ∠A is 30°.

Final Answer :-

∠A = 30°

Some extra information :-

Sin A = P/H

Cos A = B/H

Tan A = P/B

Cosec A = H/P

Sec A = H/B

Cot A = B/P

Where,

P = Perpendicular

H = Hypotenuse

B = Base

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