Question

What is the value of z, rounded to the nearest tenth? Use the law of sines to find the answer. 2. 7 units 3. 2 units 4. 5 units 5. 3 units.

Answer 1

The law of sine is the nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).

The value of the $z$ is 3.2 (rounded to the nearest tenth). The option 2 is the correct option.

What is law of sine?

The law of sine is the nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).

It can be given as,

$\dfrac{\sin A}{a} =\dfrac{\sin B}{b} =\dfrac{\sin C}{c}$

Here $A,B,C$ are the angle of the triangle and $a,b,c$ are the sides of that triangle.

Given information-

The triangle for the given problem is attached below.

In the triangle the base of the triangle is 2.6 units long.

The sine law for the given triangle can be written as,

$\dfrac{\sin X}{x} =\dfrac{\sin Y}{y} =\dfrac{\sin Z}{z}$

As the value of $y$ side is known and the value of $z$ has to be find. Thus use

$\dfrac{\sin Y}{y} =\dfrac{\sin Z}{z}$

Put the values,

$\dfrac{\sin 51}{2.6} =\dfrac{\sin 76}{z}$

Solve it for the $z$,

$z=\dfrac{\sin 76\times 2.6}{\sin 51}\\z=3.2462$

Hence the value of the $z$ is 3.2 (rounded to the nearest tenth). The option 2 is the correct option.

Learn more about the sine law here;

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