Question

1. To the nearest degree, find the measure of angle A.

Answer 1

Oh I'm taking geometry right now. 
So there is a formula that helps you find the Law of Cosines.
SOH-CAH-TOA: Sine Opposite Hypotenuse; Cosine Adjacent Hypotenuse; Tangent Opposite Adjacent.
Right now we are trying to find the measure of angle A.
We will use Cosine and divide the adjacent over the hypotenuse.
So 18/20=0.9
In a table of cosines, you find the degree of the angle by using the decimal you got from dividing the adjacent over the hypotenuse. The closest to 0.9 is 26 degrees so the answer to the measure of angle A is 26 degrees.

Answer 2

Answer:

(1) Option A is correct , The measure of angle A = 26°

(2) Option D is correct, The measure of angle B  =70°

Step-by-step explanation:

(1)

In a right angle triangle figure-1 ,

* Hypotenuse(H) is always opposite the right angle and it is always the longest side of the triangle.

* Adjacent side (B) is the non-hypotenuse side that is next to a given angle A.

* Opposite side(P) is across from a given angle A.

To find the Angle A we use the Cosine ratio:

Cosine ratio states that the ratio of the adjacent side of a right triangle to the hypotenuse.

By definition of cosine ratio we have;

$\cos A = \frac{B}{H}$                      ....[1]

In the figure - 1 we have B = 18 in and H = 20 in

substitute these in [1] to find angle A

$\cos A =\frac{18}{20} =\frac{9}{10} = 0.9$

or

$A = cos^{-1} (0.9)$

⇒ $A \approx 26^{\circ}$

therefore, the measure of angle A is,  $26^{\circ}$

(2)P

In figure -2

Find the measure of angle B.

First find the side BC, using Pythagoras theorem;

Pythagoras theorem states that in the right angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Apply Pythagoras theorem in rt. angle ABC;

$AB^2 = AC^2+BC^2$

Substitute the values of AB = 5.1 cm and AC =4.8 cm to solve for BC

$(5.1)^2=(4.8)^2 +BC^2$

$26.01 = 23.04+BC^2$

Simplify:

$BC^2 = 2.97$ or

$BC = \sqrt{2.97} =1.723 cm$

Now, find the angle B, using tangent ratio;

Tangent ratio states that the ratio of the Opposite side of a right triangle to the adjacent side.

$\tan B = \frac{AC}{BC} =\frac{4.8}{1.732} =2.772$

$B = \tan^{-1} (2.772) \approx 70^{\circ}$

Therefore, the measure of angle B is; $70^{\circ}$.