What is the approximate measure of angle R?

Question

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Answer 1

Just from eyeballing the drawing, the sides are almost equal adjoining the right angle (lengths 20 and 21), making it almost an isoceles triangle, so the angle R will be close to 45°.

Answer 2

There are a couple different ways to find your answer. I always found it best to use the "Law of Sines" whenever possible. In this case, it is.

First, you need to find the length of the hypotenuse (side corresponding to the 90 degree angle). Use the Pythagorean Theorem:

a^2 + b^2 = c^2
20^2 + 21^2 = c^2
400 + 441 = c^2
841 = c^2
c = sqrt(841)
c = 29

Now, the law of sines states:

The length of one side divided by the sine of it's angle is equal to the length of another side divided by it's angle. This is shown in your case as:

[ 29 / sin(90) ] = [ 21 / sin(R) ]

The reason why the law of sines works well, is because the sine of 90 degrees is equal to 1. This gives you the following result:

29 = [ 21 / sin(R) ]
[ 29 * sin(R) ] = 21
sin(R) = 21 / 29
R = sin^-1(21/29)

Use a calculator to get your final answer. Make sure the calculator is set in degrees, not radians. The Law of Sines can be used to find an unknown angle or an unknown length of a side. It can also be used for triangles without a 90 degree angle. Just set up the side/sin = side/sin as before, as cross-multiply to find your variable, whether it be an angle or a side.

Answer 3

The triangle is a right triangle, therefore, you can use the Pythagorean theorem to find the third side. I relabeled the sides from left to right as (B, C, A)

a^2+b^2=c^2
20^2+21^2=c^2
841=c^2
c=29

Next, use the law of cosines to approximate the angle.

b^2=a^2+c^2-2ac cosB
21^2=20^2+29^2-2(20)(29)cosB
441=1241-1160cosB
-800=-1160cosB
-800/-1160=-1160cosB/-1160
.6896551724=cosB
B=46.39718103
B is approximately 46.4 degrees

I hope this helps!! :)

Answer 4

since sides of lenght 20 and 21 almost equal
angle(R) and angle(l) are almost the same
sum of angles in a triangle is 180 degrees
therfore 90 degress + R + l =180 degrees
R + l = 90 degress
R approximately equal to l
therfore
2*R = 90 degrees
=> R = 45 degrees

Answer 5

Using the pythogorean theorem

hypotenuse = 20² + 21² = 841

hypotenuse = 29

using sine = side opp/hypotenuse

sin R = 21/29 = 0.724

R = 46.4°
.

Answer 6

The previous answers are decent approximations, but saying that it is 45° implies that the triangle is isosceles, which it is not.

So, if you actually do trig, it would be arctan(21/20) = 46.4°

Answer 7

It will be just more than 45 degrees

Answer 8

You must use cosine, tangent, or sine to solve this equation.
tangent=opposite/adjacent
tan(R)=21/20
tan(R)=1.05

Answer 9

43.6

Free trig. Calculator
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