Question

Given right triangle GYK, what is the value of tan(G)?

1/2
square root 3 / 2
2 square root 3 / 3
square root 3

Answer 1

we know that

$G=60\°$

The value of the tangent is equal to

$tan(G)=\frac{sin(G)}{cos(G)}$

remember that

$sin(60\°)=\frac{\sqrt{3}}{2}$

$cos(60\°)=\frac{1}{2}$

substitute

$tan(60\°)=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$

$tan(60\°)=\sqrt{3}$

therefore

the answer is

square root 3

Answer 2

Answer:

(D)

Step-by-step explanation:

It is given that GYK is a right angled triangle, which is right angled at K and the measure of the angle G is 60° and the measure of the angle Y is 30°.

Now, from the ΔGYK, using the trigonometry, we have

$tanG=\frac{sinG}{cosG}$

Now,the value of $sinG$ is :

$sinG=sin(60^{\circ})$

=$\frac{\sqrt{3}}{2}$

And, the value of $cosG$ is:

$cosG=cos(60^{\circ})$

=$\frac{1}{2}$

Now, the value of $tanG$ is:

$tanG=\frac{sinG}{cosG}$

$tan(60^{\circ})=\frac{sin60^{\circ}}{cos60^{\circ}}$

$tan60^{\circ}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$

$tan60^{\circ}=\sqrt{3}$

Thus, option D is correct.