Question

Help me with this please

Answer 1

Answer:

cosine∠R = 1/2

Step-by-step explanation:

We have to find the figure of triangle.

We have to find the cosine∠R.

First we find the base of triangle.

We have formula: Hypotenuse² = Base² + perpendicular²

Hypotenuse = 20

Base= ?

perpendicular = 10√3

Applying formula we get,

Base = √20² - (10√3)²

base = 10

As we know that :

cosФ = base/hypotenuse

cosine∠R = 10/20

cosine∠R = 1/2 is the result.

Answer 2

Hello!

The answer is:

$cos(R)=\frac{1}{2}$

Why?

Since it's a right triangle and we need to know the adjacent side of the triangle, in order to find cos(R), we can use the Pythagorean Theorem.

Pythagorean Theorem formula:

$c^{2}=a^{2} +b^{2}$

Where:

$c=hypotenuse=20\\a=FirstTriangleSide=AdjacentSide\\b=SecondTriangleSide=OppositeSide=10\sqrt{3}$

So, the adjacent side will be:

$AdjacentSide=\sqrt{c^{2}-b^{2}}=\sqrt{20^{2}-(10\sqrt{3})^{2}}=\sqrt{400-100*3} \\AdjacentSide=\sqrt{100}=10$

Now, that we know the adjacent side, we can calculate cos(R), so:

$cos(R)=\frac{AdjacentSide}{Hypotenuse}=\frac{10}{20}=\frac{1}{2}$

Have a nice day!