Question

Please help!

Answer 1

Step-by-step explanation:

We are given two angles measures and one side. Notice the given angle and the side that is opposite to that given angle is given. We need to find side x. But can we also find the angle opposite of the side we are trying to find. Yes we can

Remeber that triangles interior angles add up to 180.

Remeber that triangles interior angles add up to 180.One angle measure 90 and the other measure is 57 so

$90 + 57 + x = 180$

$x = 33$

So the angle opposite of the side we are trying to find is 33.

Since we know two angles and two sides that are opposite of those two angles respectively, we can use what is called Law of Sines

$\frac{b}{ \sin(b) } = \frac{c}{ \sin(c) }$

where the numerator are the side measures, and the denominator are the angle measures.

Plug in the respectively values. Angle 57 is opposite of 10 and Angle 33 is opposite of x.

$\frac{10}{ \sin(57) } = \frac{x}{ \sin(33) }$

Multiply both sides by sin 33 to isolate x.

We get

$x = 6.494$

Round if needed

In other words, apply law of sines when you have two angles and two sides that are opposite of those angles respectively.

Answer 2

Answer:

x = 6.5

Step-by-step explanation:

In order to solve this problem, you need to use trigonometry (sin, cosine, tangent).  

Sin = opposite/hypotenuse

Cosine = adjacent/hypotenuse

Tangent = opposite/adjacent

We need to use tangent in this case because 10 is the opposite side from the 57° angle, and x is right next to it, making it adjacent.  So, our equation would look like this:

tan (57)° = 10/x

Multiply both sides by x

x (tan (57)°) = 10

Divide both sides by tan (57)°

10 / tan (57)° = 6.49408 = 6.5