Question

For the right triangle shown, which expression represents the length of CA?

A) 7 sin(40°)

B) 7 cos(40°)

C)

7

sin(40°)

D)

7

tan(40°)

Answer 1

Step-by-step explanation:

The attached figure shows a right angled triangle right angle at C. It is required to find the length of CA.

Here, CA = x = perpendicular

BC = base

AB = hypotenuse =7

Angle B is 40 degrees

We know that the ratio of perpendicular to the hypotenuse is equal to sine of angle.

$\sin\theta=\dfrac{P}{H}\\\\\sin(40)=\dfrac{x}{7}$

x is length of CA

$x=7\sin(40)$

So, the correct option is (A).

Answer 2

Using trigonometric relationship, the length of CA can be obtained uisng the relation CA = 7 sin(40)

• The the length of CA is opposite the angle 40° given ;

• The other length given is the hypotenus of the right angle triangle.

Using SOHCAHTOA :

The opposite and the hypotenus are related to the sine of the angle.

Hence, we have ;

• Sinθ = opposite / hypotenus

Sin(40) = CA/7

Cross multiply

CA = 7 sin(40°)

Therefore, CA = 7 sin(40)

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