Use the diagram to answer the question. Triangle R S T. Segment R S measures 10 units Segment R T measures 8 units. Angle T is a right angle. What is the measure of ∠R?
If you need the answer specifically it's 36.869. But if you need the answer rounded the answer is 36.9.
Well, it looks like we're dealing with a right triangle here. And you know what they say about right triangles... they're always right!
Since angle T is a right angle, that means it measures 90 degrees. Now, we can use the good ol' Pythagorean theorem to find the length of segment RT.
The theorem says that in a right triangle, the square of the length of the hypotenuse (RT in this case) is equal to the sum of the squares of the lengths of the other two sides (RS and ST).
So, let's do some math! If segment RS measures 10 units and segment RT measures 8 units, we can plug those values into the equation:
RT^2 = RS^2 + ST^2
8^2 = 10^2 + ST^2
64 = 100 + ST^2
ST^2 = 64 - 100
ST^2 = -36
Uh-oh! It seems like we've stumbled upon a problem here. The square root of a negative number is not defined in real numbers. So, it appears there might be an error in the diagram or the given measurements.
Since we can't determine the length of ST, we can't determine the measure of angle R either. Looks like this triangle has decided to be a mystery, just like its sides!
To find the measure of angle R, we can use trigonometry. Since angle T is a right angle, it forms a 90-degree angle. We can use the Pythagorean theorem to find the length of segment ST.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, segment ST is the hypotenuse, and segments RS and RT are the other two sides.
Let's substitute the given values into the Pythagorean theorem:
(Length of RS)^2 + (Length of RT)^2 = (Length of ST)^2
10^2 + 8^2 = ST^2
100 + 64 = ST^2
164 = ST^2
Taking the square root of both sides, we can find the value of ST:
√164 = ST
ST ≈ 12.81
Now that we know the length of segment RS (10 units) and the length of segment ST (approximately 12.81 units), we can find the sine ratio of angle R:
sin(R) = Length of RS / Length of ST
sin(R) = 10 / 12.81
sin(R) ≈ 0.78
Next, we can find the measure of angle R using the inverse sine function (sin^-1):
R ≈ sin^-1(0.78)
R ≈ 51.06 degrees
Therefore, the measure of angle R is approximately 51.06 degrees.
To find the measure of ∠R, we need to use the information given in the diagram.
First, let's recall some properties of a right triangle. In a right triangle, one of the angles is a right angle, which measures 90 degrees.
Looking at the diagram, we see that angle T is a right angle. Therefore, angle R is the remaining angle in the triangle.
Since angles in a triangle add up to 180 degrees, we can use this information to find the measure of ∠R.
∠R + ∠S + ∠T = 180 degrees
We know that ∠T is 90 degrees, so we can substitute this value into the equation:
∠R + ∠S + 90 = 180
Now, we can simplify the equation:
∠R + ∠S = 90
But we don't have the measure of ∠S given in the diagram, so we cannot directly solve for ∠R with the given information.
Therefore, with the given information, we cannot determine the exact measure of ∠R.
review your basic trig functions and it is clear that
cos R = 8/10
so, ...